1981 corvette running lights stay on when key is off

you may have a vacuam hose off somewhere, else adjust the throttle plate stop on the carb where the linkage comes to rest

could be a bad brake light switch which is mounted near the brake pedal under the dash try adjusting the plunger which contacts the pedal maybe its on going in far enough otherwise replace the brake light switch

you have to bleed system

what you could start with is checking to see what trouble codes are being logged for this vehicle...if the engine light stays on, it means the ecu is registering a fault......by the means of a trouble code...now the trouble code doesnt tell you how to fix it, but it does give you the direction to go down...judst wondering if you have tried to obtain the trouble codes

take out the ash tray its under there.

Start with dirty fuse connection and then look for mouse wire damage

I would ahve the alternator tested to see if it was bad first, if so I would replace it and see if that improves your choke situation. If the alternator is not putting out enough voltage it can affect other systems in you car including an electric choke system.

You got a check engine light viewing. If so get the shop manual make youself a jumper wire and jump the terminals it tells you to jump and count the flashes for the codes. The ECU/ Brain terminal is under the ash tray. If there are no codes or a check engine light welcome to the wondeful world of being a Corvette owner I 've owned the same car since 1981.
Basically, check the idle,you may want to replace wires, Distributor cap and rotor. Thats worked for me in the past. Once the PCV valve was stuck. Pull it out and shake it if it rattles its fine. You can blow thre it to has to accept air one way but not the other. The shop manual will tell you to do the same.I believe they may go a step further and recommend an oil change and minor cleaning of the carb. I use mine for shows and because I don't run it regularily I get the same problem. I usually let it run for a few hours (ideling of course) lol... and it works itself out . Keep me posted

you will need to pull off the four retaining nuts holding seat in place. Measure the length and width of bottom support frames. Many seats are interchangable.

you will have to remove the master cyl no need to dissconnect the lines and dissconnect the vacuume line and from inside the car under the dash dissconnect the brake pedal from the shaft running to the booster. and remove the 4 mounting bolts that hold the booster to the firewall and pull foward in the engine compartment.
as long as you dont dissconect the brake lines you wont need to bleed the brakes.
good luck
paul