Exactly. A relay kit should get rid of your "turning off" issue, as well as most likely brighten up your stock lamps very noticeably.
As said too, the new H4 lamps are an upgrade in themselves. If you're still running truly stock type incandescent sealed beams, then the difference is literally night and day. If at some point in the past one of the PO's upgraded to halogen sealed beams, then the difference will depend on what quality light they put in at the time.
But the relays are definitely an upgrade over stock wiring. Still running my original '71 switch that was giving me trouble 25 years ago just like yours. Put some uprated H4 bulbs in and was playing around with the high-beams when it started. Good wiring (for it's age) but couldn't handle the extra wattage of my 55/100's!
![Wink ;) ;)](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
;D
Paul