1991 Dodge Caravan transmission not engaging?

OK, the "back story" is we bought this van used and cheap about 18 months ago. It "must" have had a replaced transmission, I think, as I've never heard of a Caravan transmission holding up this long--but the previous owner, who'd had it about a year, didn't know.

It's done remarkably well. The "usual" electrical problems (for an older Caravan)--speedometer and gauges work intermittently, warning lights randomly go on and off, interior lights mostly don't work, wipers and door chimes randomly go off, stereo doesn't work most of the time, etc. But DRIVES really well. :)

Also, since the odometer only works intermittently (like the speedometer), the mileage is a guess--but I feel like it "must" have at least this many miles, and I'm guessing at least 50,000 on the (presumably) replaced or rebuilt transmission.

Recently (last month or two), sometimes (not every time--no discernible pattern) when I go from Park to Reverse or Park to Drive or Reverse to Drive or Drive to Reverse, nothing happens. It's like I'm still in Park (or Neutral?--I haven't done a "roll check" because I'm usually in a spot where I need to move).

So far, this has corrected when I put it into Park, wait a few seconds, then put it back into gear. The last few times, it's taken me doing that a few times before it "got with it" and engaged.

There's no audible odd sound/change, no loss of gears when driving that I've noticed, etc. I've had transmissions go out before on both manual and automatic, and they didn't go like this--instead they "lost gears" until all were gone and the car acted like it was in neutral when it was in gear.

I've searched online and the only reference I've found is for a Toyota doing this and the answer was a "internal hydraulic pressure loss = a major transmission problem" unless it's a selenoid in which case the check engine light would be on. Well, due to the electrical problems, I can't tell if the check engine light or any other warning light is on. If it would ever do it in the driveway I would put that fuse in (I've pulled several, including the one that controls that awful "ding" sound when it randomly decides the doors are open and they're not) and see--but a check engine light would still be pretty meaningless, I think.

Any thoughts? Is there something simple we can check or change first? If this is the transmission going, is there a likely pattern or timeframe?

We hope to get a new van in a few months--we don't want to finance and we want to get a nicer used model--but probably don't want to put the money into replacing the transmission on this one. OTOH, we have kids so I CANNOT be stranded somewhere if it's preventable!

THANK YOU!