You say it doesn't have any codes, but didn't say which module you tested. 4x4 operation is controlled by the GEM that year, so make sure you test that.
The flashing lights mean the shift requested by the control switch wasn't completed. The pinpoint test in the manual for this problem is many pages long and requires the use of a scanner with live data monitoring. In the end, you most likely have a problem with the shift motor, wiring, or GEM, in that order.
Some people disassemble the shift motor, clean all of the internals, and get the system working again so that may be worth a try as it costs nothing but time.
It won't be a fault in the hub system, as there is no feedback built in and the GEM isn't capable of seeing the status of the hubs. It is a blind system.
1970 Mach I H-Code...
Well, that's what all these pieces are supposed to resemble.