Head light switch has an internal breaker, they get weak with age, put the H/L head lights on relays as an upgrade.

If both headlights are blinking at the same time, I’d suspect the headlight switch, or dimmer switch.  Check the wiring plug connectors before replaced the switch.  Could be a problem with the ‘dirty’ connection, clean connections with a contact cleaner.  Best to use “DeoxIT”, to deoxidize to contact points (available on Amazon).  I’ve used this on several connections with good results.
You can also use an eraser (like on a pencil) to clean male stabs of connectors.

 

The headlight switch has a breaker that resets itself thus causing the blinking. Does it do this on both high and low beam. Is the breaker getting weak, try unplugging the headlights. If it still clicks (blinks) I'd say you have a short. (May need a test light to plug into the headlights to see if you can't hear the light switch click) If a short is suspected first guess is the High/Low beam switch. It's already mounted to ground. You could also unplug at the beam switch and do the previous test.

If you are running modern headlight bulbs you need to install relays for the headlights,  They draw too much amperage and trip the breaker in the headlight switch.  I had the same issue.  Went to relays and never looked back. 

Someone might have a P/N for a "Kit", but for the cost of your email address I'll send you a quickie diagram so you can buy some parts and build your own, if you are so inclined.
BB1