Couple of things...
Get some SeaFoam, run it through the fuel tank at least once per month, and you will never have fuel-related issues again (it dissolves varnish, stabilizes gasoline for up to 12 months, absorbs water, and some other stuff which won't matter one bit...); if you do this, you will never have varnish clogging up your carburetor jets again, period. Run the SeaFoam through the crankcase (search this forum for "Seafoam", and you will get quite an eye-full of stuff to read) and transmission, to dissolve varnish, sludge, and carbon deposits within the engine and the tranny, left over from the SF-rated oil, used back in 1980 -- when the SeaFoam has done its work, the oil will turn black, change it, and the filter. Modern, SN-rated oils, will not leave deposits behind, if you change oil on a regular basis (3,000 miles conventional, 5,000 miles for synthetic).
Check the spring on the rear brake pedal (FSM has diagrams showing its location). Sometimes this is lost, or stretched, preventing the lever from coming back up to its normal resting position.
Change out the front fork fluid -- it likely is anything but cherry red in color (Dexron color; fork oil is light caramel color,when new), which is what it should be. The FSM explains the process, but I did not disassemble mine, or remove them from the bike -- I just used the drain screws. This is the most overlooked maintenance issue on any bike. The good news is that Honda used Dexron III ATF in the forks, which runs around $5 per quart; fork oils run around $15 per quart! The Dexron works very well, it is inexpensive, and it is available everywhere.
Support the engine under the front, with a jackstand; add 2 oz. of SeaFoam to each of the fork tubes before draining, compress the fork tubes by lifting the front wheel up/down, around 10 times, to circulate the SeaFoam inside the fork hydraulic systems, which will dissolve varnish/crud; remove the drain screws on the outside, bottom of each tube, and carefully collect the old fluid which will run out (read the FSM instructions, before attempting this modified method). Compress the fork tubes again, to push out as much fluid as possible, then re-install the drain screws, and tighten just beyond snug. Re-fill the fork tubes, as per the FSM, with fresh Dexron ATF (III-VI is all good, but the VI will be synthetic, and a bit more money -- but it will last twice as long). Changing the fork fluid every two years is a good schedule -- it does wear out, over time, and miles.
The suspension is more than just comfort on the ride -- it keeps your wheels tracking the road surface, as opposed to flying above it! Poor maintenance of the suspension system can lead to loss of control, and... Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII