Whether a drill auto-restarts or not is decided when placing or
upgrading it. There is a 30% chance that the drill becomes an
auto-restarter and always restarts 5-20 seconds after jamming.
Otherwise the drill does not benefit at all. Auto-restarters may jam
several times, but will always fix themselves until they are finished.
Upgrading or repairing a drill does confer the chance only if the
auto-restart icon is not shown already (which itself does not indicate
whether the drill is an auto-restarter or not). Thus you always have
exactly one chance for the drill to be an auto-restarter. If it is
not, it will never be.
Source: The Long Guide - Remarks on Technician Skills by Frankelstner (emphasis mine) (info are taken from extracted game files)
All drills have a 30% chance of being auto-restarters with the skill. That means that if it restarts once, it will always restart itself after a while. There's no way of telling if a drill is an auto-restarter, besides waiting and checking if it restarts or not.
Auto restarters are coded to restart after 5+rand*15 seconds, or 5-20 seconds, if they successfully got the trait. If it doesn't restart automatically after 20 seconds, it never will.
... If [the drill] won't restart, you'll usually get some kind of audio queue from a heister telling you to fix the drill if it's been long enough.
Source: Related posts on Reddit /r/paydaytheheist by users Menolith, KarateF22 and Shadeol, supporting the information quoted from the Long Guide above
The HUD mod, HoxHud (PC only) can give an indication whether a placed drill has an auto-restart chance. Without a mod, as mentioned above, there's no way of telling if a drill is an auto-restarter, besides waiting and checking if it restarts or not.