Tecumseh part number for the link rod is #32698 You choke lever looks correct and someone may have just twisted it over at the top a little to clear the exhaust. you can verify its correct by looking to see f it has a flat spot ground into it between body and lever which should rest against the stainless tab that serves as a detent to hold it in the open/run position. on the HS40 with that carb it typically sits in the open/run position right above the air filter and pulls to the right to choke.
I cant tell if you exhaust is sitting to low or ??? That carb was very short lived during 1971 model year, your engine model number should be HS40 55331c and probably very late 1970 or very early 1971 serial number. They were coming out with the angled intake and bowl carb to replace the diaphragm setup and clearance for the choke lever on the new 1971 models with exhaust on the right of the bike rather than crossing over to the left was not good with the diaphragms.
A diaphragm carb needs to be totally disassembled to properly clean (that means the welch plug on the side and the one, on that particular version, found covering the main/high speed circuit check valve, under the diaphragm itself There is a non serviceable brass check valve under it that main welch, you can pull it out but you must make sure its very clean in there. you fuel also has to be squeaky clean since there is nowhere for dirt or debris to go but into the circuits. so if you tank has any problems you always going to have problems even with good filters.
That is the correct carb for your engine and, if original, is unique to the slanted application HS40 only, It was the ONLY diaphragm that ever was built, setup, and used for that size engine and only used 1969-early 1971. You can verify by looking at the number stamped in the mounting ear which will be stamped 356, if its stamped 379 than its from an H25-35 and the idle circuit is totally different and much smaller so it may not want to run correctly/well I just finished a full engine resto on a similar early '71 slanted application HS40 for a member with the same setup. and I just found another one of the HS specific 356 carbs which just came out of the cleaning solution and I will be rebuilding, great and hard to find carbs!
Here it is during break in
this is one I did a few years ago that is the same version as yours:
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