It’s been quite a while now and I haven’t seen any reports of actual conflict between the IDF and the Lebanese military, which would tend to suggest that they’re staying out of it altogether.
For all of the talk of cease fires and peace keeping forces, who would actually do it? The US is busy in Iraq, and the last time we tried that it didn’t work out too well anyway. Most of the available European forces (small in number to start with) are with NATO in Afghanistan. Assuming that part of some eventual deal involves “peace keepers” (technically more peace keepers, there have been a number of ineffectual UN troops there for years.) where would they come from? The Arab countries? China, Russia or India perhaps?
Or will that be a negotiating ploy used to delay a cease fire until the IDF weakens Hezbollah to the point where the Lebanese military takes over, which might be a very long time.