Yes this serial number is hard to find much info on and that happens from time to time.
I can see serial number 1A061105 comes up as 6.2L B 6R D07 14P 6.2L MPI DTS, Model Number 40620062T which in this case the model number isn't coming up as expected either to help with another way of locating parts using the exact numbers that's usually preferred so in this case you have to look for the serial number range which I was able to find that fits your engine model in the following link,
https://www.mercruiserparts.com/mx-6-2l-mpi-bravo-0w650000-thru-1a2999
1 - 2 minutes of dry run time especially on a Bravo style rubber impeller is very much too long and the impeller is most likely pretty damaged up and needs a new one even if it was brand new to start out... Most will replace their impellers every year just to be sure while others may push 3 years or until an issue arises... Here's your impeller pump system,
https://www.mercruiserparts.com/bam/subassembly/31958/12840/270