IF they are adjacent, the #8 and #10 should be on different legs which would create a 240v circuit and blow one or the other, and possibly the main breaker, if they were connected together. The same with #12 and #14. This is a valid assumption since your pool pump is 240v and it uses adjacent breakers. Something is erroneous in your diagnosis. You could safely connect #8 and #12. And #10 and #14.
Thank you hj. I embarassingly have typos in my very pretty diagram. It's actually 8 and 12 connected and 10 and 14 connected. Do you have any ideas on an application that might have required this? Security systems or cameras perhaps? I would just really like to know why they did this before I bring an electrician out here to make it safe.