Can't tell where to enter on ProConnect until it is clear what the character of this income is.

Sounds very much like this is one of those ad-hoc arrangements that employers make with employees, often with flawed logic and without consultation with a tax advisor or legal counsel.

Based on the limited info you provided, these payments in relation to the termination of your client's employment should constitute wages.  The regs are very clear that remuneration for services, unless excepted by the statute, constitutes wages even though at the time paid the relationship of employer and employee no longer exists between the person in whose employ the services were performed and the individual who performed them.

In other words, a W-2 should have been issued each year for these payments and FICA along with FIT/SIT should have been withheld.  If the intention was to fund the insurance premium on a net basis, FICA, FIT, and SIT should have been grossed up.