Moist salt air near coastal areas is rough on aluminum. Your photo shows outside skin on stabilator. I wonder what inside of wing, stabs, and tail cone look like. Biggest problem is where skins overlap, seams, and skin attachment to underlying structures - these are natural trap for moisture...
Scrub it with gray scotchbrite and Bon Ami. Rinse well. Dry. Spray some rattle can SEM or NAPA 7220 on it. That should protect it till painter does his thing.
Alumiprep is great but almost impossible to rinse it out completely. It's a strong acid.
To determine the depth of the corrosion, you could start with a simple metal polish like Nevr-Dull to remove the surface blemishes. I had rodent-induced corrosion on a few stored parts. The polishing helped identify where the corrosion had gotten through the alclad, and needed attention. https://www.amazon.com/Nevr-Dull-NEVER-DULL-POLISH/dp/B00097CRY6
Scrub it with gray scotchbrite and Bon Ami. Rinse well. Dry. Spray some rattle can SEM or NAPA 7220 on it. That should protect it till painter does his thing.
I agree you need to prime these pieces. Be careful however about putting any paint and/or primer on the exterior surfaces. If you know what paint you will use on the exterior (or your painter of choice knows) use a comparable primer. This will save you time (or money if using a painter) as prepping to correct for a bad/wrong primer is a pain.