Trying to verify that Arduino Pro Micro ISP is working
As Mikael Patel notes, pin 10 on the programmer Pro Micro should run to RST on the target.

That might or might not fix the problem.  In some previous instances of the “Yikes! Invalid device signature” [1,2] bad breadboard connections turned out to be the problem.  I suggest you run a second (or even a third) set of jumpers in parallel with the first set.  Of course use matching colors to avoid confusion.