On my 93 EGlide my headlight goes out when riding but spot stays on

 

Check grounds and ensure clean and tight connections , free from corrosion.

 

Start with your light bulb and confirm that the holder is clean and dry, also the holder makes a good connection with the bulb. Take care is it will get hot, but turn it on and see if, when jiggled, it stays bright. Then work backwards along the wires to check for sound connections, ground etc. Electrical problems of this sort are often mechanical, in other words two parts of the circuit are not working together as they should. Also check your rear lights, just in case.