1988 Chevy Truck Wiring shortages

Electrical problem
1988 Chevy Truck 6 cyl Two Wheel Drive Automatic

I have a 1988 Chevy Silverado C1500 it has had a different engine put in remote entry and a toggle start button all put on in it before I got it Its run great since I got it 6 months ago. But in the last few weeks I've been having problems with interior lights staying on after I turn it off, heater coming on every time I turn ignition on, and controls on the stereo not working at times and stereo just plain not turning on or off. The other night my son was going to take it to work and we had just received a large amount of snow so he unlocked the doors started the truck turned on the lights and got out to clean the truck off and shovel out while it warmed up. When he got and shut the door it locked. We tried using the remote but even with new batteries it didn't work. The truck end up running for quite some time before the lock smith came in fact it had died. We jumped the truck got it started battery gauge read a strong 14 to 15 started again 6 or 7 times off and on but in the process of jumping it and repeated starting lights would stay on, heater wouldn't stay off stereo stayed on or came after it was turned off. And 10 to 12 hours later it's completely dead again not even a click. We made sure everything had turned off the last time we turned it off so I'm fairly certain nothing was on or running. So my question is where do I start to track down the problem?Is it possible the remote is shorting out?I know there are a million things it could be and I'm just wondering with all these things happening where to start?The extra wiring is all tied up tight, and covered it looks very neat or professional so I have no suspicious spots or melted or hot looking wires. Any suggestions or advice would be appreciated.