If anything, what you'd be looking for is the _absence_ of language restricting claims to work done using the employer's facilities -- but whatever's there real

If anything, what you'd be looking for is the _absence_ of language restricting claims to work done using the employer's facilities -- but whatever's there really needs to be read in context of the whole agreement, and the applicable state law. There's no phrase search yet that can substitute for a lawyer with relevant knowledge.