Ok Geddy scientists, please help me out ...
I believe Geddy used the Rick (almost) exclusively in the 70's through Permanent Waves and for most of Moving Pictures but then in the mid 80's-on I get lost on what has Wal, Steinbeger and Jazz ... and when did he go back to the Jazz in the 1990's?
Chronology please?
As far as I know it's like that: I don't know whether he used the Jazz already on Permanent Waves, but to my ears, it sounds like it's always been the Ricky.
On Moving Pictures you hear both basses. Alembicplyr was right with the examples he gave.
On Signals it was the same. On some tracks the Rick, on some the Jazz. To give an example, but I don't have any evidence for that, I'd say that on Digital Man, he must have used the Jazz, whereas the bass you hear during the pre-chorus, the chorus and the solo of Subdivisions is the Ricky, but as I said, it's just what I guessed by listening to it, there's no evidence, probably we'd have to ask Ged about it.

When recording the Grace Under Pressure album, he switched to a Steinberger headless. As far as I know, it has been used on all tracks of that album exclusively, but on some tracks (his Rickenbacker appears in the Body Electric video though), there might be bass synths. Some of the bass on Afterimage sounds a little like that to me.
Before recording the Power Windows album, Geddy got into playing Wal basses. He would continue to use them on all records following records, Hold Your Fire, Presto, Roll The Bones until he got back to the Jazz for Counterparts. In this period, he would occasionally use fivestring basses as well. One thing that always makes me wonder is why the Wal on Power Windows sounds so different compared to the other recordings of that period. Did he use a totally different bass, set-up, rig or whatever? Any informations on that?
However, coming to your question when and why he went back to the Jazz. The first recording on which he used his old used Fender Jazz Bass from the seventies again was Counterparts. Rush wanted to do a rock album again but as it turned out, the Wal wasn't too well-suited for this purpose, so being given the advice by his bass tech he pulled out the old Jazz Bass again and used an old Ampeg amp they found in the studio which he turned up as high as he could at the risk of blowing it. Since then, Geddy has stayed with Fender and ordered several Custom Shop basses you hear extensively on the Test For Echo album and which are used today for certain songs live, especially if another tuning is needed.
Edit:
@skb5string:
Wow, didn't know he used the Rick on Grace Under Pressure and the Steinberger on Hold You Fire. Do you have any specific song examples?