Most likely in the UK are Paterson, Philips or Kaiser timers. In general, all timers will have a switch for focus/timer -- at least I've never seen one which doesn't . . .
Forget getting anything clockwork, on grounds of precision and repeatability. They may have been tolerable when new -- but thirty years later, after decades disused in a damp shed, not so good.
There are electronic timers with one dial, for example Durst TIM, but these might be tricky to set precisely at the bottom end of the range. Ideally you want something that you can set in tenths of a stop and for small enlargements (and hence short exposure times) this will mean precision of well under a second. A useful and practical style has three dials, one each for tenths, whole seconds and tens of seconds. Other models have a switch for "x10" while using one dial, hence two time ranges on one control, which can also be an adequate solution.
The switching off of the safelight when the focus-switch (and also timer, usually) is active comes from the historic use of enlarging-meters which are sensitive to the safelight as well as the actinic light of your enlarger, therebye giving a false reading and requiring the safelight to be off during measurements. Probably you have no enlarging meter so this feature is not required at the moment. In the future use consistently made contact-prints as your enlarging meter, instead of another gizmo.
In "the olden days" many started off with a simple on/off switch in the enlarger cable and counting ticks of a metronome, or "one thousand, two thousand etc", which can also work perfectly well if you can avoid short exposure times.