Has it really been 10 years? Makes me feel old. I'm posting my reply to agarcia, for posterity...
"Been busy. Sorry so long to respond.
Year? Auto/Manual? Color?
Just curious... they make no difference.
Because you say, "It's wired, but not connected to anything," I believe your left mercury switch is the problem.
It works much like the thermostat in your house... When the bubble gets to the programmed position (ie: 68 deg), it makes contact and tells the furnace to turn on. Same here, except it tells the computer, 'good-to-go.'
You can hold a switch in your hand and test it with an Ohm meter: Vertical = No continuity; Horizontal = Continuity (might be the other way round).
When the seats flop down, both mercury switches make a connection. So the switches must be hard-mounted to the back corner of the seats where the spring-bar is pinched.
The spring-bar has too much tension. Many are broken and only one seat flops down correctly. If yours isn't broken, I might suggest cutting it in half with a grinder at the exact center point. Then there's less tension on each 1/2.
While you figure it out, you can operate the top manually: Open the trunk, find the pump in the right quarter and open the brass T-valve. When you manually lift/lower the top, hydraulic fluid flows through the pump-bypass circuit. Then close the valve. Be careful to not crack the brittle plastic hoses!
The convertible top system uses a separate / custom computer module. It's located behind the dash just to the right of the steering column; a silver box possibly held closed with duct-tape. It monitors all related circuits including the Speedo: If you're moving more than 1 mph, the up/down switch won't work. You can hear the box 'click' on/off if you listen carefully when stopping/rolling at a stop light or downhill. Be sure you don't imagine the box part of the stereo system and unplug it.
FYI: There are parts you can scavenge from a 1986+ vert, which is easy to find. These include the rear seatbelts. The rear courtesy-lights are found in the cargo area of a 4-Runner.
The stereo system w/ a third speaker is a unique animal. As an audiophile at heart, I know you'll never get really good sound from the factory system and there's not enough room for larger speakers anywhere in a Celica. (The dash speakers are 3" and no one makes them. There was a Pioneer TS [something]. But I prefer a graphite cone and rubber surround. Just make sure your new 3.5" speaker has a mount-corner which can be bent to fit.) If you replace the head deck, best to route new speaker wires (16 ga. min) to all four corners and ignore the third woofer in the dash. The original system requires the 'amp-box' bolted to the tunnel floor behind the ashtray because all speaker grounds run through it. You can't really tap into it and the 25 amps (watts) available from any aftermarket head-deck will sound better anyway.
I also suffered the battery discharge problem: It was a faulty voltage regulator in the brand new alternator I bought. Didn't get to it for a year and just bought another Alt. Problem solved! Diagnosing unwanted drains is a pain in the tuchus: You have to install an Ammeter at the battery+ and search for the drain one circuit at a time with schematic in hand, ie: Clock memory is not unwanted. It's a miniscule load and takes a year or more to drain a battery.
Enjoy your Vert!"
