Hose connections to Intake Manifold
 

On my 2002 two wheel drive there are two hose connections to the back of the intake manifold (by firewall). When looking from the front , the one on the right has failed (split at top bend). I cannot find where the other end of this hose goes. Following it with my hand, it appears to go back under the firewall. This split is causing periodic rough idle (and sometimes stalling). Can't find hose listed anywhere for replacement. Any ideas?

Could go to the IMRC, Intake Manifold Runner Control

Google: 2002 ford ranger Intake Manifold Runner Control

Don't think so. Pictures of the IMRC show just a vacuum line (too small). Also, when engine was rough idling in the driveway, I heard a hissing sound and felt around with my finger. When I crossed the split hose, my finger was sucked to the hose and the idle immediately smoothed out. The hose around the split was very oily, suggesting some kind of crankcase ventilation.

Split head hose connected to intake
 

I have the same problem right now, but I can’t find the name of the hose anywhere. I was told it was the PCV valve at first but that’s completely different. Do you know the name of the hose with the split head?
thanks
https://cimg5.ibsrv.net/gimg/www.ran...c03bd2ae5.jpeg
https://cimg1.ibsrv.net/gimg/www.ran...b74847bdd.jpeg
Vacuum leak coming from the split