Unemployment eligibility?

I’m just curious about unemployment (not expecting to use it…) and want to know if a second job which is a part-time non-contract faculty position would make me ineligible should I ever need to use it.  Currently I work full time as at a firm and teach at most one course per term as an adjunct faculty member for a college I’ve been affiliated with for three years. Should I loose my broker position, would this part-time appointment render me ineligible to receive unemployment benefits? My contract assumes 10 hours per week of “work” (not necessarily in-class) at an hourly rate.