I have an old Craftsman garden tractor (mid 80's) with a Briggs 18HP twin with no spark. The engine model is 422437. Confirmed that the coil is bad (it is open). I have tried several new coils(part # 394891), set air gap for .010, still no spark. I test for spark with the kill switch wire disconnected on the coil. The replacement coils do not exactly match the original. There is no metal pad pickup on the new coils. My manual shows a second coil called a trigger coil but I do not see one of these on my engine. I would appreciate any suggestions.

I'd replace the coils with a Magnetron replacement (Part#:  394970)  . 
No points, just bolt down:
 
https://www.propartsdirect.net/Parts/Kit-Magnetron-Ign__394970.aspx 
 
.

My engine does not use points or have the 394970 trigger coil. It uses coil 394891.