Attach the new object to the rubber "outlet" on the side of a rubber tree and it will harvest the rubber whenever it it respawns. Right click to access it and take the Resin out. Requires power.
If the "harvest when it respawns" thing is too hard, it could just produce Resin on a timer that is equal to the respawn of normal resin outlets.
Reason is that if I'm at a point where I have all this high-tech automated machinery, automatic mining machines, etc. with buildcraft pipes doing all the work for me, I still have to go around with a bunch of wooden treetaps and manually collect a bunch of rubber.