Ideally call for start a few minutes prior to EOBT...at peak times, however, this is unlikely if there have been, say, weather regs all around the patch.
If the CTOT delay is 0 minutes and pilot calls for start after EOBT then ATC will assess whether aircraft can still make the CTOT.
The CTOT time should be regarded as the time aircraft are #1 at the holding point and ready for departure.
The CTOT window (-5 to +10mins) is for ATC to best manage departure order (e.g. departure routes, aircraft speed groups, wake turbulence).
It's not uncommon at "smaller" airports (with short taxi times, e.g. 5-10mins) when delays are present, that pilots request start just before CTOT with an expectation that they can be airborne before CTOT+10.
If there is no other traffic ATC might take the risk and give start approval at/just before CTOT (3-4minutes to start + 5minute taxi + 1minute to line-up and depart = 9 or 10minutes).
In all likelihood though there will be other traffic, there will be taxiway delays, there will be a number of other aircraft which have called in good time to make their CTOTs, etc, etc.
So, ideally call for start just before EOBT (but only call if you are actually ready!).
In practice call for start by CTOT minus the taxi time minus a few minutes for start up. That way ATC should have at least 10 minutes of "slack" for unexpected delays and to juggle the departure order to achieve the most efficient operation.
The most important thing is that if you know you're not going to be able to make CTOT (do not rely on CTOT+10) get a DLA message in early. The earlier you can adjust your expected EOBT the better the result will be for your new CTOT. If you leave it to the last moment and ATC refuse your start the likelihood is you'll get a pretty hefty CTOT delay.