Grindelwald-Kleine Scheidegg & Swiss Travel Pass

I’m just a bit confused on trying to sort out whether I can take the train from Grindelwald to Kleine Scheidegg using my Swiss Travel Pass. Planning a visit in early October, and using Lucerne as a base. My wife & I took a ski trip to Grindelwald several years back and always wanted to return in the off season, so this year we’re going to do that. In checking the SBB timetable, I can find the various train times between Grindelwald & Kleine Scheidegg, but when I tried digging deeper, the only pricing information I found was for those holding Half-Fare cards (15.50 CHF one way).

So, does the Swiss Travel Pass cover the Grindelwald to Kleine Scheidegg train, and is that a different type of train (cog)? – Although I rode it once, frankly I forget since I was too busy looking at the scenery. We did the special train from Kleine Scheidegg to Jungfrau during our winter visit – very impressive going through the mountain by the way – and won’t be doing that again, but I’m glad we had our ski jackets on for that.

Would it be better to head towards Kleine Scheidegg via Wengen? We never did see Wengen.