For certain, Eschew feats (and other caster-specific feats) are not available when taking a Fighter bonus feat. Only feats that apply specifically to Fighters can be taken during a Fighter bonus feat level.
I'm pretty certain (90%+) that they aren't available when taking a non-caster level at a usual feat interval, but to be honest, it's been ages since I took a fighter level with my multi-classed caster.
Is this for build planning or is the character about to level? If the latter, you can just start the process and see what it gives you and cancel out before finishing. If it's the former, the safer assumption is that caster-specific feats are not available when taking a non-caster class level.
It's something I'd have to test to be 100% sure about. Perhaps someone else has more recent and/or vivid memories.