Personally I wouldn't trust either fix.

That roof is protecting how many thousands of dollars in framing, drywall, decor and etc.?

replace the perforated shingles with whole shingles, properly installed. save the patches for the underlay.

Sure you will pay a roofer for a mornings work and the shingles might not match perfectly but water damage from roof leaks goes on for a long, long time before you notice it in the house...usually.

Also, the roofer might discover that you've had undetected leaks around those mounting bolts. A good inspection is in order after removal of those panels.

Agreed. Replace, not repair.

It is best to repair a break in a roof shingle by placing a metal sheet under it. The stuff you put on top is temporary and/or essentially cosmetic. Mother nature is not kind to roof patches.

I like to take a shingle tab. if your shingles are 3 tab. slide it under the shingle with the hole. then tar the hole. you might need to cut the top 2 inches off the tab and remove nails to make it fit. for the best look tar the hole from the bottom.

I agree with others make sure there has been no water damage around the holes. if there is, the repair the sheating and put new shingles down.

-dkenny