Can you Rez an upgrade during a run? And when?
You can rez an upgrade anytime the "Rez" symbol appears on the timing chart for the structure of a run.

This is mostly the same as when paid-abilities can be used, there are a couple of paid ability windows where you cannot rez cards, the most notable being the "Encounter" window with ICE.

From the rules, this is timing sections 2.3 and 4.3. Also before and after every action.

1. Runner starts, names server.
2. Approach outermost ICE.
2.1. Paid ability
2.2. Jack out (goto 6) or not
2.3. Approached ICE can be rezzed
     Paid ability can be used
     Cards can be rezzed.
2.4. Check if ICE is rezzed.
3. Runner Encounters Ice if rezzed.
3.1. Icebreakers can interact
     Paid abilities can be used
3.2. Resolve all unbroken subroutines
     If run hasn't ended, and there's another piece of ICE, goto 2.
     If run ended, goto 6.
4. Runner approaches attacked server
4.1. Paid abilities can be used.
4.2. Jack out (goto 6) or continue.
4.3. Paid abilities may be used
     Cards may be rezzed.
4.4. Run is successful. Trigger abilities if any.
4.5. Access cards. Trigger abilities if any.
5. Run ends. Trigger abilities if any.
6. Run is unsuccessful. Trigger abilities if any.


If there isn't any ice, you won't have the 2.3 timing window, and so you can only rez your upgrade at the 4.3 timing window.