My 1935 12 gauge Tournament grade is choked WS1 and WS2. On occasion the left barrel will not fire after the right. The left ejector is sticky as well and will sometimes not eject. Is this something I could try to tackle myself with disassembly and cleaning? Guessing there might be a few years of crud built up. Or is this something better left to a competent gunsmith that understands 21s? If so, any recommondations? Thanks.

I would try some ammo that has a little more umph. Failing that a strip and clean would be the first thing to do. Also provides an opportunity to inspect the internals for any breakage or wear. These guns are stout and usually very reliable.

If this doesn't do the trick, get it to a good double gun 'smith.

I hate single triggers on a SxS gun.

The 21 is a mechanical single trigger. So it shouldn't matter how much recoil or any to make the second bbl fire after the first.

There is a counter weight in there to protect from doubling, but it has nothing to do with switching the trigger over to the other bbl/sear after one is fired.

Like any SST, they can be very frustrating to work on. You'd think just removing the stock, reassembling without it and watching what happens when you pull the trigger would instantly tell you the problem(s). But it doesn't work out that way.
The very slight tension applied by the tang screws to the tangs and trigger plate effect the placement of the trigger parts with the stock in place as opposed to having the stock removed. The lower tang often bends or flexes the most.

It's a tricky gun to disassemble all the way to just parts and also to reassemble. Especially the mainsprings, hammers and the single trigger assembly.
The top lever spring and small spring guide can give you fits when reassembling too but it's still easier than a Fox.

The ejector forend assembly is pretty straight forward.
You can take that out of the wood as a complete unit and clean it as such if you want to. Then re-lube.
They come apart quite easily. The only part to watch for is a small roller that sits inbetw the 2 kickers. It's free to roll away on you once you drive the cross pin out and pull the kickers out of the forend iron.

More then likely 85 years worth of dried oil, dust, dirt, power residue.

I would take the stock off spray it down with a good cleaner until clean then oil the action.

Put it back together and try it.