My old battery died, so I had to use a battery charger/engine starter to start the truck. While the battery was weak, I noticed what seemed to be strange behavior ...

My old battery died, so I had to use a battery charger/engine starter to start the truck. While the battery was weak, I noticed what seemed to be strange behavior with the lights. During darkness, while the truck is off and parked, the blue high beam indicator on the dash stays on all the time except when I open the door or start the motor. The daytime running lights do not come on at all at any time. Sometimes during daylight the low beams come on automatically and with the front parking and rear taillights just as they would at night. The interior map and dome lights seem to be doing bizarre things. Both dash buttons (rear cargo light and dome override button) either alternate at turning all of them on or off, or no matter which dash buttons are pushed, no interior lights will come on. A good new battery is in the truck now. The alternator checked out okay when the new battery was installed, but the issues with the high beam indicator staying on during darkness when the truck is off continue as does the interior lighting weirdness, and I still have no DRLs. My regular driving lights come on automatically when it’s dark as they should. I disconnected the battery for over an hour in an attempt to reset the computer, but that didn't change anything. It didn't even wipe out my radio presets. Any comments or ideas on what's wrong and what probably needs repair/replacement

Did you possibly hook up the charger incorrectly the first time? Check your cables to make sure they arfe not corroded. Sometimes they will corrode under the insulation and not look bad from the outside. See if the cable looks a bit wider, or big around near it's end. If so, that is an indicator that there is corrosion inside the insulation and the cable will need replaced.

^This
Also when you disconnect the battery to try and reset the computer, press the brake pedal until the tailights die out. That should drain any remaining charge left in the system.

Thanks for the replies.
Rule out corrosion and a reversed connection.
I left the battery disconnected for well over 5 hours this time. I left the door open to keep the interior lights on, which promptly went out when the battery was disconnected. I depressed the brake pedal anyway for over three minutes. I still have the same radio presets and unfortunately the same problems with lights.

Here's some additional information. The truck was left parked for two or three months at a time, after which the old battery was dead and had to sit for several hours with the charger set at 10 amps to recharge it to where it would start. The battery tested good. Then one day, the truck was driven for about three hours with some stops and restarts without any problems. The last part of that trip was at night, so the headlights were on. The truck still had no problem restarting that night. The next day the truck would not start at all, even after hours of 10 amp charging, because the battery had finally died. The truck would just make the typical weak battery clicking noise that was followed by a high pitched whine after the key was turned to off. It took a 50 amp boost to start. It was then driven for about three hours without stopping to get back to the city for service. During that trip there were no lights for the odometer and the gear shift indicator. The lights on the radio were also out for about the first two hours of that trip and very weak during the last part. It was some time when the truck was getting the low battery from sitting and then having to be recharged that the lighting problems developed that I originally described. I had hoped the new battery would make it all better, but it didn't. I have had good lights for the odometer, gear shift, and radio since replacing the battery, but the other problems I've described persist.

I'd have the new battery and the alternator checked again just to make sure they are good. Other than that I'd check the grounds.

After several weeks, things are much better. The instrument panel problems just went away on their own. The high beam indicator quit staying on while the truck is parked in the dark. All the lamp switches and buttons are working properly now. I found posts on other sites about the DRL bulbs both burning out at the same time and that they should be replaced in pairs. Simultaneous burnout seemed unlikely to me before reading that. New bulbs solved that problem. Everything is working properly now, and all I had to do was wait several weeks and install two bulbs.