I applied for my unrestricted license in PGY2 in the state I was training in (only requires 1 yr of GME), and I applied for my unrestricted license in the state I am planning to move to in PGY4 (requires 3 yrs of GME). The latter I didn't get until PGY5, straight up took 6+ months.
I'm very happy I did that. It's a requirement for graduation and board certification, which I don't have to worry about. Pretty much every job I've interviewed with has asked about it, and when they assumed I didn't have it, they looked at it as something that would delay my start, because it delays credentialing.
My advice is always to get it as soon as you're eligible. That way you have it in hand, and if something happens in training, you at Ieast are licensed.