If you're only using Tcas 1 [less than 30 seats?] no specific action is authorized as a result of a tcas alert other than to have BOTH pilots looking out of the windows to visually acquire the target
a TA in tcas II is the same thing as an alert from a TCAS I system [legally] in that case your objective is to SEE AND AVOID---assuming VMC.
In IMC query the relevant controlling facility about any known traffic in the area and perhap if outside of busy terminal airspace switch modes TA---TA/RA if you feel a genuine collision threat is possible
And if there's an RA, well I'll assume you know what to do.
It would be incumbent on both crew members to deal with this situation!
edited to add: where the heck is ADS-B already!!!