Automatic door locks

Hmm, if memory serves, this is a programmed function, though it's been a while since I've had a Lumina. Looking in Prodemand and AllData won't turn up anything, because they generally focus on bigger issues. But I thought that it was set up where the car would lock automatically when you put it in gear, and unlock when you put it in "park" or something along those lines. As far as disabling the function, there's no known way to do that other than to pull the fuse for the power locks. But that would completely disable the power lock system, so even the fob wouldn't do anything.

As it turns out though, my father-in-law has a 1999 Lumina. I can call him up later on and ask him how his works. That'll shed some light on the mystery.

Haha about the key. I have a pull string set up on my 2002 blazer that pops the rear glass open. As for my father in laws car, his doesn't auto lock or unlock at all, but the power locks do work when you push the button. I suspect his not functioning might have something to do with the ignition interlock device on his car.

But having it auto-lock when you start the engine is odd. I've never seen a GM do that, and I only buy GMs. I suspect you may just have some sort of odd problem in your car's Body Control Module, the computer that controls such functions. Does your car have any other quirks? Maybe the security light stays on? Or maybe the cruise control doesn't work. Anything like that.

By chance, does the car have an aftermarket security system? Because that would explain a lot of things. To disable that, you'd have to find the guts of the thing and unhook it.

That key fob is an aftermarket replacement, probably purchased off of Amazon or Ebay for a few bucks. An OE one would say "trunk" on the trunk release button, not "GM." Plus the buttons aren't even a little worn off, like they normally would be on a twenty year old fob. If I had to guess, I'd say that the button in the middle has something to do with syncing it to the car.

As others have told you, I can't seem to put my finger on exactly what's going on. An educated guess would be that it has something to do with the way that fob is programmed to the car. Perhaps re-syncing it would help. Check this video out for instructions: https://www.youtube.com/watch?v=b81j97xZ7PE

And here are actual written instructions: https://blog.keylessentryremotefob.com/2013/12/1999-chevrolet-lumina-key-fob-remote.html

Give it a shot is all I can think of right now.

Hate to be the bearer of bad news, but that remote is one of the ones used on a dealer installed "accessory" alarm system, not one that was the built in factory option. The OEM factory installed Lumina remote is the 3 button unit in the attached image.

The dealer installed item was a 4 button remote from Directed Electronics that controlled the DEI after market alarm and key-less entry unit. The small "button" in the center of the remote you have should be a red and green LED that responds differently depending on which options are installed and enabled in the control box. It is somewhat of a generic unit that dealers sold as an upgrade and was installed by them on vehicles that didn't have the factory system or that didn't have an alarm with the factory system to give you key-less entry and an alarm, The 3 second auto-locking option is a DEI common feature. The second image shows a section from a model 425 guide showing that option.

Most of the DEI units have a model and serial number that can be looked up to get instructions on the unit. The OEM units like yours are adapted from one of their consumer models and sold strictly to dealers. They included branded remotes to make them look like a factory item but they really are not. Some used internal switches to select the options, others use a programming switch and the remote to program options and they also had units that used a special programmer box to set the options.
The controller will be installed under the dash, usually tucked up in the wiring or taped in place. It will have 3 to 4 wiring plugs on it that connect it to the vehicle.

DEI has been around a long time, they make the Viper, Python, Auto Start and many more alarm and remote start units. https://www.directed.com/

If you can get the information off the unit it should be possible to get the info. DEI is pretty good about support. Removing it is an option but you would need the installation manual to be sure where each wire went. It is piggybacked onto the OEM system but some wires do get cut and if you missed one you could end up with worse problems than locking doors.

The click would be the park interlock solenoid. Keeps you from putting the car into gear without your foot on the brake. You can thank the folks who drove through houses and stores for that item. As they wear the plunger moves a bit farther until you hear the internal stop get louder as the plastic on it wears.

Steve and his vast amounts of odd information never ceases to amaze me. Nice work Steve! At least I was right that it was an aftermarket (albeit dealer installed) system and remote. Anyhow, I defer to Steve on this subject, as he clearly has the experience with this setup.

After dealing with a few hundred of these things installed by the "professionals and dealers" in this area I will withhold my full opinion on them, suffice it to say that it is somewhat lower than a snakes belly.

As for finding the who behind may of the systems the FCC ID on the outside will usually get you better information that the part numbers. If you open the remote up like you are changing the battery there are many that have the makers information on the circuit boards as well.
Your FCC id starts with EZS which is a DEI code, Then the OEM which says it's a dealer installed item built for a particular company. The part number tells you the OEM in this case is GM.
There are a few companies that do these for the OEMs. The question then becomes "Was the guy installing them any good?" In this I have seen everything from a quality install where the wires were trimmed and soldered with self seal shrink tubing and the unit installed on a bracket with proper materials. Others were full length wires with connections made with scotch locks and zip tied in place and the lowest forms had the wires just twisted together and taped with the units just stuffed up under the dash behind the harnesses and just hanging there.

Same things happen these days. One of the first things I look for on security or no starts is an after market remote start or alarm. Most have no real testing options so you look at the wiring and what it connects to and try to bypass them as needed.

You're welcome. We will be here if you have any other automotive questions.