I left it elsewhere and brought the Makita 3601 to weigh it so can't check at this time. You grab a little thing pull it out and then press the pulled out thing forward. Then when the trigger is touched it moves to normal run. A down push kills the engine just like my Dolmar 6100 say. I doubt there is a solenoid think it is linkage, it does have a throttle cable not linkage. The day I brought it home it restarted quite well now it restarts quite reliably holding the throtle full on and drop starting, not so reliable any more just pulling the rope. I don't have a 339xp to compare it to but the 338 top handle new edition one with the automatic compression release and crude one transfer port per side starts incredibly well and I have never removed the limiters. It sure does not have the dirt and air separation of this new one.The husky auto tune mark 3 version doesn't have a choke position just a start/fast idle position. The choke is set automatically by the mk3 software. I have the 540xp mk3 which has auto choke and I believe the new 592 has the mk3 too.
There is no ipl available for the 540mk3 but you can go to the Husky website and get to the pages one at a time and order parts of that if you are really curious if a solenoid on the choke. Like the battery chainsaw I have not all the electric parts are shown maybe the dealers can get a few more pages. Part #21 is called choke control assembly (carb and air filter sheet if it does not bring you there directly) and https://shop.husqvarna.com/us/EPCProductView?epcOverrideCategory=Chain+Saws&catalogId=13051&epcProduct=540+XP®+Mark+III&epcVariantName=540+XP®+Mark+III&modelId=&epcCategory=Chain+Saws&epcBrandName=&csfId=&langId=-1&storeId=11251&epcPmid=A00001640#