The Welch Allyn 490 Green Series Minor Procedure Headlight frequently has problems with the DC power connector at the end of the cable which attaches to the battery. Upon requesting information from Welch Allyn tech support on a source for a replacement connector, I was basically laughed away. So in an act of vengeful kindness I did a bunch of research, and here is the information on the correct replacement connector.
It is manufactured by Switchcraft.
model: 761KH
datasheet: https://www.mouser.com/datasheet/2/393/761KH-766KH_CD-1110840.pdf
link to product on mouser: https://www.mouser.com/ProductDetail/Switchcraft/761KH?qs=sGAEpiMZZMtnOp%252BbbqA0023axwHuElQykQKvTZQ%2F%252BL5jFIxL1TlIDA%3D%3D