The Hi Lo switch contacts can get "strange" with age. They need a bit of "wiping" action to keep the internal contact oxidation at bay. If it improves with operating the switch several times, that could be you issue. Same is true for the Off-On switch if yours is so equipped.
The Starter button is also in the control path for the headlight, as it turns off the headlight while the starter motor is engaged. I've found this switch handles the current draw of the stock headlight with ease, until a leaky master cylinder bathes it in brake fluid. Then the plastic housing inside disintegrates. After that, starter engagement and/or headlight function can be unreliable.
I have rebuilt 3 or 4 of these switches. An alcohol bath of the remaining pieces and super glueing them back together, has restored them to proper operation. It is a tedious job, though. And, you have to like puzzles and be adept with the cya glue nozzle. There are also two spring loaded balls in there to juggle back into proper position. Some plastic safe grease is also required. It lubes the switch and also holds the springs and balls in place during reassembly of the switch. I've never seen any indication of the switch contacts being overheated, as would be the case if it was overloaded.
