Very old unit. Probably needs a new carb or at least a carb rebuild kit installed. They have carb kits with everything on ebay for about $25.

I've got a couple of Homelite Bandit SX-135 (UT20601). Bought the first in 2001 as a cheapy to back up my Echo SRM2100. Had problems with running to lean and ended up prying off the mixture screw limiters to allow for richer mixture. Also added Seafoam to the fuel to gradually dissolve out the gum. Got almost 20 addition years out of the machine. Been keeping the second as a parts machine.

As for the choke, easiest thing to do is take off the air cleaner cover and remove the piece of foam. You should be able to see the choke butterfly and by moving the lever you can now see the "run" position and the "choke" position.

As for the string head, mine came with a single string .065 head. I ended up transplanting a dual head and winding it with .080 line. I don't bother with the bump feed; rather I momentarily shut down the engine, and manually advance the line. With the heavier line and dual string I can go quite a ways without advancing line, unless I am working around a chain link fence or edging against concrete.

Thanks for the comments. I did as you suggested and now know where the choked and unchoked positions for the carburetor are. Biggest issue, once running, is that the butterfly valve in the carb has a tendency to close which causes the unit to start losing power. I ma getting pretty adept at catching it before it kills the engine but surely think this should not happen. If I knew repalcing the carburetor would cure this issue I would order a replacement but don't want to start spending for a lost cause. As for the string head, I have also, knock on wood, had pretty good luck with respolling and having the bump head dispense line on the fly.

The SX135 Bandit came with either a Walbro WT-458-1 or Zama C1U-H41 carburetor. Both carbs had a detent feature on the choke to provide a "RUN" - "HALF CHOKE" - "FULL CHOKE" positions. This is done with flats on the choke shaft and a spring and ball assembly. If the choke shaft rotates freely without resistance at the three points, someone lost the ball or spring during reassembly. That would explain why the choke won't hold the full open position.

You're going to have to disassemble the carb to see what's missing and either purchase the necessary parts (if available) or purchase a carb from Ebay or Amazon. Make sure you get the correct Zama or Walbro item.