Yes 3 times a second will be ok, but 5 times would be better
standard 5999 resolution would be enough.
For the uni-t multimeters, I had one, on which you can disable the auto off, but it needs to be done on each power up, and while it won't turn off, it will beep for each 5 minutes
A lot of people does not know, but same feature exists in PeakMeter, Fnirsi and lot of other Chinese multimeters.
And for disabling I meant once and permanently - for example, in these FeelElec multimeters, this is done via menu - and there you can even select the default measurement type on power on.
None of these have manual range on their selector.
I mean, there are no separate positions for say 0-2v, 0-20v, 0-200v, 0-10A and so on.
So I need traditional DMM, with everything clearly on dial, but no auto off and backlight constantly on.
I've modified PeakMeter PM18C to have constant backlight, but no always on feature (except you press the hold button before power on and it will then beep each 5 minutes).
My mistake, I missed the words "with Manual Range".
That narrows the search down to manual ranging multimeters only.
And the only one that comes to mind and almost covers your requirements is the cheapest one available, some variant of D830. You only need to install one or two LEDs in there. I don't think it has an auto power off feature.
If you don't want to install some form of backlight yourself, you may need to look for an old manual ranging DMM with hard on/off switch and build in backlight. But you may still have to modify it to keep the backlight constantly on.
There may be some but I don't know of any manual ranging meter built with programmable features like changing APO and backlight timers.
There are quite a few manual ranging DMMs available from some manufacturers. As far as I know, all these new multimeters have that annoying (to some people) meter ON reminder, where meter beeps every few minutes to remind that APO is off. This is not a function built by the DMM manufacturers. It is a feature made into the DMM chip by the chip manufacturers, instead.