We love Illwinter!

[thejeff]

Have you tried, once they lose the rhythm, conquering a few new provinces and trying to set them searching again? Preferably provinces lower in number than your capital.

Also, if you set one to search the capital, does the next one also target the capital, or move to the next unsearched province?

My results have been consistent. A searcher picks the lowest numbered unsearched non-capital province. Except that sometimes capitals are targeted and some other provinces are skipped. But it's consistent about that, too. A skipped province is always skipped and a targeted capital is always targeted.
I'll generally just let them search the capital if they want to. It's a waste of gems and time, but it lets me keep using the auto-search.