Whether a student qualifies for/receives TE, you have to do FAFSA correctly. The parent who provided the most financial support to your son in the last 12 months is the FAFSA contributor. It has nothing to do with which parent the son lives with more. If the two parents each provide exactly 50% financial support, then the parent with the higher income and assets is the FAFSA contributor. (Note there are limited guidelines as to how to calculate financial support. Just be able to document/support whatever you choose to do.)
https://studentaid.gov/apply-for-aid/fafsa/filling-out/parent-info
Also for FAFSA, it doesn’t matter which parent claims the student as a dependent on their tax return. Many divorced parents alternate claiming their kids as a dependent, and that does not impact who the contributor is (it’s always the parent who provided the most financial support in the last 12 months.)