I don't really understand your question, and I guess that no-one else does either?
As far as I can tell from the web, the Basilisk unit is nothing to do with timing. I assume that any midi data that comes in to it, will go out? If appropriate. But normally, you press the foot switch and pre-set midi data in the unit goes out and does whatever it's supposed to do.
Timing is not relevant. Except as to WHEN you press the foot switch?
Of course, the drum machine may be quite different. You don't say what this is, and you don't say what the other unit is that you mention that MAY have some relevance to timing (another drum machine, a sequencer ?) But as far as the devices that prob SHOULD be co-ordinated then maybe you need to investigate if one of them can be timing-controlled by the other. It may not matter which way around, so whichever way is more conveniend/easier to achieve.