After following every thread here I can't exactly find this problem, so...
Have a 1994 ls400, 158,000miles, was in a front end collision at 120,000 and has been running great after repair until ~ 4000 miles ago would stop while driving (at highway speed) and then could be started up right away again. This has been getting more serious until last month it stalled and could not be started until the next morning. At this point it continues to start after it has not been run for several hours or overnight and then runs several miles - stalls and sometimes starts right up, sometimes not for several hours!

So, thinking electrical, this weekend I replaced plugs, wires, distributor caps and rotors. Found that the left camshaft sensor wire was being severely abraded (likely by fan belt) to the point where the two wires were exposed and shorting - nearly intermittent. Fixed that. Also, per several posts, pulled throttle body (yep, it was carbon city) and cleaned it as new. Put it all back together - started up straight away - filled the gas tank and went ~ 10 miles then stalled - same symptoms - started ~ 15 minutes after stall but would not idle and stopped. Started again after several hours and got it to idle - very rough initially -then ran for about 15 minutes at idle - went to shift it from Neutral to Park and quit - would not start up (no CEL during any of this, btw).

Also, since the front end collision, the shifter has been difficult to get back into Park - its a bit mushy and have to push on it a bit to get it to click.

Maintenance has been quite regular - timing belt replaced twice - and typical problems have been encountered and dealt with, i.e. - PS problems fixed - dashboard lights/electronics fixed.

What might I look for next? (Fuel, TPS, ...?)

 

i had the exact same problem, change the fuel pump

 

Well, yes, the fuel pump was indeed on its last legs - kind of sputtering when I tested it out of the tank - so changed this out as well as the fuel filter - and contrary to some of the opinions I have heard from toyota the filter was full of sediment which was absolutely in need of replacement (previous replacement was @80k mi (~75k mi ago).

Nevertheless, this did not fix the problem. So looked through ignition again - and found EFI fuse body to be cracked with a partially severed fuse link - so replaced this and then got CEL 41. Yep, TPS was indeed bad - ohmed it out and found sporadic and non-repeatable resistance. Replaced this with new and behold runs like a charm. Put in fresh battery and have had 5k+ trouble free miles since!