::..not sure what happens if Trump just never signs it.::
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Isn’t that called a “pocket veto”?
I believe you are correct.
Article 1, Section 7 of the U.S. Constitution states:
If any Bill shall not be returned by the President within ten days (Sundays excepted) after it shall have been presented to him, the same shall be a Law, in like manner as if he had signed it, unless the Congress by their Adjournment prevent its return, in which case it shall not be a Law.
Actually, in the case you specify, the bill would become law, since if the bill is not signed for ten days, while Congress is in session, it is the same as if it were signed. If the Congress recesses before the 10-day period is reached then the bill would be vetoed on the 10th day while the Congress is still not in session. That would then be a pocket veto.