This is very common.
A track that follows a main road (For example, the Yagur-Yokneam highway has a bicycle/walking track all along the road).
I’m wondering if I should add a separate track in these cases (It obviously has different attributes).
Illustration of a track thing by benkatz100, on Flickr
Absolutely.
If one would want to navigate in “Cycle” or “Pedestrian” mode, the routing program will try to avoid motorways, and the existence of a separate track/path will be essential in this case.
dimka
It depends.
In this particular case (if I remember correctly) there is real separation between the road and the track.
So there should be two different ways (actually, the road is separated, so it has 2 ways already, each with oneway=yes)
However, if it’s on the same place, e.g. Shvil Israel near Shizafon, then there’s no reason to add another way, and the primary road should be “cut” into smaller segments, with the relevant ones being part of the relation.
Or just look at this, which is worth a 1000 words… 
talkat.
Okay. Got It.
BTW - This is what I did (In progress…) on this specific road.
The ways are so close that they seem to merge in some parts which looks unaesthetic to me but it’s just a rendering issue I guess.
It’s a renderer thing.
Osmarender renders thicker residential, tertiary, track, as can be easily seen in that link.
Mapnik shows it nicely separated if you zoom in.
talkat.
Interesting something I read on the osm questions forum regarding this topic:
link
Specifically notice:
Yes, but think of places outside of Israel, e.g. The Netherlands.
There, it is normal to have cycleways along highways, so you use cycleway=track to note the cycleway “of that highway”.
In the case that you’re referring to (Yagur-Yokneam), there’s a track (agricultural?) that is not related to the main road.
They are 2 separate beings, with lives of their own.
At least, this is how I see it.
talkat.
I see your point…
Makes Sense.