Indeed you have come to the right routine, but not easy patch it, because it makes multiple passes through the same routine in the update. And if it gets patched in a loop.
The routine checks if there is an older firmware or newer and performs the update in both cases, matching up the firmware version and then delete the file gupdate.

Would have to install a counter, which always perform the update once, the second time would enter the comparison function normal, and logically verifying the same firmware version installed and gupdate file.
Do not know if it will be worth.