1987 Toyota supra turbo

If you ask the owner for the faults he has had expect an out right lie as to nothing is wrong with the vehicle. With such low mileage better to ask why he is selling it. I suggest that the seller produces proof that he actually owns the car and is capable of selling it legally. Next take it for a good run ( not around the block) and be critical in listing all noises and problems you find. Next take it to a reputable mechanic for a frank appraisal of the faults and see what he comes up with. Any must do repairs should be deducted from the asking price as you will be stuck with that cost.. Considering the age and the listed mileage I am suspicious that the mileage has been tampered with as most cars average 15 to 25 k per year Be very cautious also because the parts supply for an 87 car has dried up and you will most likely only get second hand parts ( Panels)

motor shot

A stock anything will not be the fastest thing around. I've seen some pretty wicked 1100+ supras though. Your answer in part would be the 98 tt supra it will run a quarter mile in about 13.3 seconds

Brake light fuse , or burnt out bulb , or switch on brake pedal.
The bulbs have 2 filiments in them , 1 for running lights and 1 for brake lights.

Best bang for the buck is going to be airflow. As in cold air intake and exhaust upgrade.

you will need an additional turbo manifold. I have the correct one its for sale right now on eaby. The ct26 turbo manifold does not allow for proper mounting. I can include directions with the manifold

should be behind the timing cover and behind the timing belt.

1987 non-turbo: 10 deg Before Top Dead Center (BTDC) @700 rpm
1987 Turbo: 10 deg BTDC @650 rpm.

To set the timing, you will need to connect a jumper wire between terminals E1 and TE1 on the diagnostic terminal. This diagnostic terminal is located just aft of the engine compartment fuse box. It is a black plastic box marked "diagnostic" on the cover, which flips open to reveal the terminals inside. There is a diagram on the inside of the cover which explains the terminal positions. On the Turbo model, you need to remove the forward section of the engine cover to gain access to the number one spark plug wire.

Yes. However it is a very expensive swap $5000 to $8000 to do it right. You will need the 1J or 2J engine, transmission, wiring harness, ecu, and alot of other pieces to do the swap. The engine brackets will need to be modified and you will have to upgrade your brakes. This kind of swap requires a good knowledge of the Toyota Supra and the engines. I do not recommend this swap for a beginner. A cheaper way is to take a 7M-GTE and upgrade the internals and turbo.

Is it a turbo? You may be having a fuel-cut issue. Has teh problem happened since? If this only happens once is a while, it will be hard to diagnose.