I bought an 83-TR1 in oktober 2003 an has renovated it to original spec. Has some small things left like the rear turn signals that shall have a new holder. It had been left outside for a couple of years i think! With a good polishing equipment the aluminium on the engine soon started to gleam again! I have spent about 200 euro on it and it runs great! The carburettors were cleaned, the battery changed,the saddle repaired, a new (used) exhaust system (BSM),a little more grease in the chaincase and that's it!
See pics;
http://www.buf-online.kristianstad.se/~lars.sandstrom/mcfix.htm
The saddle on the 82 and 83 TR1 are more comfortable (thicker and softer padding) than on the 81:s.
The bike has a lot of low end tourque and about 70 hp on top, fairly light (ca 240 kg full tank) and has good suspension so it's great fun to ride!
The most important things to get it to run smooth and agile is to balance (syncronize) the carburettors and to have the correct air pressure in the tyres.
Go ahead an by it!
Regards Lars.