Anyway, you should probably experiment with creating a multi-column index instead of allowing PostgreSQL to BitmapAnd them together. Likely the timestamp will have higher cardinality and so should be listed first in the index.
No, the timestamp should almost certainly come second because it is used with inequality operators.
Wouldn't that only matter if a typical inequality was expected to return more rows than a given equality on the other field? Depending on the cardinality of the ID field I would expect a very large range of dates to be required before digging down into ID becomes more effective. My instinct say there are relatively few IDs in play but that they are continually adding new rows.
What statistics would the OP have to provide in order to actually make a fact-based determination?