When do I execute a missed approach on a LOC approach when I can't identify the MAP?
Well, I’m not an FAA guy so I can’t find the relevant FAR quote, but going more general:

ICAO Doc 8161 Vol 1 - Aircraft Operations I-4-6-1

6.1.4 Note 2


  In the case of a missed approach with a turn at an altitude/height, when an operational need exists, an additional protection is provided for the safeguarding of early turns. When it is not possible, a note is published on the profile view of the approach chart to specify that turns must not commence before the MAPt (or before an equivalent point in the case of a precision approach). 


There is a nuance difference between AIM’s “you are not supposed to turn” and the ICAO’s  “if the turn area is not protected there must be a warning label”. The first is just procedural, the second ensures you will not hit a mountain. 


If the missed approach only specifies ‘Climb 1000’ then climbing left turn to..’ then the airspace is protected even for early turns (between IAF and MAPt) and you can start turning as soon as reaching 1000’. It might get you in trouble with ATC (ie. they were not expecting you to do it), but it will not get you into a mountain side. If you can call ATC and explain that you are turning early because of a navigation/timing fault, you will be allright.
If there is also a ‘do not turn before [...]’ then you shouldn’t turn before, regardless if that fix is the MAPt or not. How to determine that fix or MAPt then becomes a navigation issue:can you use alternative methods? Gps? Dme? Vor radials? are you under radar contact? How about using the VSI climb rate to estimate 1 minute (climbing 700’ at 700 fpm). If neither, then you might be in an emergency situation.