Since you have ignition, the thermal fuse is not involved, coils were a possibility, the thermistor, was a possibility as if it was the black one they were flaky from day one.

Does this pattern happen at same intervals when a load is in it? The burner does not stay on for long, it cycles on and off in normal usage. When empty the burn time is pretty short. It's a function of airflow primarily.

Observe the burn, is a small jet of flame escaping toward the hi limit thermostat on the top of the burner tube? Look for burns around the opening for the hi limit or signs that it is getting hotter than the surrounding duct. Sometimes the flame spreader (or "spoon") sags over time and allows flame to leak around its sides and prematurely open the hi limit. Also the regulator may be allowing slightly less pressure through as it ages so the jet is not blown inward under it's own force as effectively.

I've been known to remove and bend the spoon slightly flatter to stop this when no other reason can be found. There's no real risk unless you severely alter that shape; and it doesn't bend that easily so it's hard to over do it.

This is the spoon. It's upside down in the pic. You may have an adjustable air shutter there also that can affect it too. But I rarely move air shutters as it controls the O2 mix and you want a clean and efficient burn.
Whirlpool WP693140 Burner Tube - AppliancePartsPros.com