It sounds like it is broke... Beseler does not use quality switches in their timers and with time they can get balky, suprising as their enlargers go forever.
A fix that may work is to get a can of contact cleaner spray at Radio Shack, open the box up and give the switches a spritz while working them back and forth. That includes the x1-x10 switch. The stuff can make a bit of a mess but all that is left behind is some mineral oil and that won't harm the electronics.
If that doesn't work I know a man who can sell you a timer ... with 50,000,000 cycle switches. It was bad switches on a Beseler timer that prompted me to start a small buisness making f-Stop timers. Bad switches and the fact that linear time makes no #$@#%@! sense when it comes to exposing photographic materials. If the microprocessor had been invented before the enlarger there never would have been an enlarging timer marked in seconds.