Are they looking for the physical pump to be there or simply the emissions they think have been raised by not having it? Other ways to resolve it if the second choice there.
And your question as posed is impossible to answer. No year, no model or engine or trans even, we don't even know if it is a Ford or not. Not helping yourself there......eve n trans type can mean air pump or not. The state does not require certain equipment other than if you are in California, i.e., there are California emissioned cars and all the others are considered '49 state' models.
I take note of the specialty insurance (b) clause as 'requiring another car to be registered and used as the mainly used vehicle'.
Here in Texas once car is 25+ years old no more tailpipe testing, only a visual check, I'm sure they only look for the cat pretty much.