No, do NOT use the glove box outlet. You'll need a POWER outlet for a compressor. The glove box has an AUXILIARY outlet, meant for small loads only. It is fused at 3 amps. This is a common mistake, don't fall for it! I have a battery tender plug wired directly to the battery large loads like this. Other people do it other ways but I'm a minimalist with such things. Be sure to experiment a bit, you may have to up the in-line fuse a little depending on what compressor you buy.
Yeah. I plugged a Harbor Freight “high power” tire inflator (I think compressors have tanks) into the auxiliary outlet in my Subaru Outback. I then got a lesson in modern oddball fuses. The outlet was fused 10A, not enough for that application
Outback has a 15A auxiliary outlet near the rear hatch. Nonetheless I bought a battery clip to “cigarette” outlet pigtail for that inflator. No risk in future.
2018 F-150 XLT SuperCab 4x4 2.7L
2016 Beta 430 RS
2016 Subaru Outback
2013 Tesla Model S 85
2009 Husaberg FE450
1983 Porsche 928S