The blinking is because the circuit breaker built into the headlight switch is overheating & opening the circuit... Once it opens the breaker cools & resets & the process begins again... The cause is likely a combination of problems... High resistance in the wiring & connections creates a higher current load to run the headlights, eventually the breaker has gotten weaker & now you are at a point where the breaker routinely fails.. The quickest, cheapest & best solution is to use the current headlight wiring to control a pair of relays... The relays only require a fraction of the power driving the headlight requires so the current headlight switch will probably be fine... Go over all the connections in the rest of the wiring & it will be fine.. just add a pair of relays, supply power to them off the battery post on the starter relay, use the current headlight wires to trigger the relays, ground the other side of the trigger coils & use the relay output to run the headlights..

"The Armies of our ancestors were lucky, in that they were not trailed by a second army of pencil pushers."