From the graphics tab you can see where Titan is for any date relative to Saturn, which allows you to guess when the next transit might be. Then adjust the day and hour until you get it right. So yes, trial and error for the first one and every 16 days after that.
One of yuzameh's links above does contain the information, but it's not completely intuitive (and is in French): https://ssp.imcce.fr...tellites-events
If you choose Saturn, and manage to fill in the other fields (I just put in degrees for coordinates - accuracy doesn't matter), it will output a list. You're looking for Corps A to be "606" for Titan transits. Eg, for June 14, you'll see two times with 606, one the start of ingress and the other the start of egress (I assume the time in minutes is how long Titan takes to cross Saturn's edge). I don't see a way to filter for a particular event, but presumably you could download the data and then filter in Excel or similar software. Creating a list of start and end times of any given event wouldn't take much work once the data are downloaded. There is a diagram under Documentation that visually explains what the Type codes mean. So PA.D and PA.F are the beginning of ingress and egress respectively. Other codes refer to shadow transits, occultations and eclipses.
As probably noticed in another thread here, I did use the documentation button at imcce recently and then something called reverso (online) to get a better idea of the column headings (cut and paste then translate). Still not entirely sure on some aspects (the flux ratio value for instance) but others work.
One thing I did notice is that Guide 9 for the first Oct 2 eclipse event differed by quite a few minutes, which was a bit weird because the June event matched within seconds (I also figured out the leap second situation, the version I've got goes back to before the 2017 leap second, and states that future values of TD-UTC will be extrapolated, so Guide is likely using 70.4 seconds (at least on my system) difference (delta T consists of a fixed TD to TAI (atomic clock) difference of 32 and a bit seconds and then you add the leapseconds to that), whereas it's only 69 and a bit because they stopped adding leap years (the planet also sped up recently and at one point they were worried about how to fit in a negative leap second, a lot of modern interactive stuff nowadays needs time not to be played with so much, so they haven't used a leap second in ages and are thinking of ditching it in 2035, as all it does is make little Y2K type issues for firmware)
ANYWAY, the real point is that when you've got your list of predictions up from IMCCE you will see at top right of the table just generated (NOT the page, the table) is a little cog wheel symbol, which usually means "settings". I bravely clicked it and found a pleasant surprise.
A list of the names of the objects generated in the table appears with little tick boxes next to them. So if for instance you unticked all bar Saturn and Titan you'd only end up with the predictions for Titan. I just unticked Saturn to narrow it down to the satellite mutual phenomena at first, but suck it and see is likely the way to go.
NB it turned out that on 2nd Oct 2024 there was another partial eclipse around my local noon, and I think at just about Saturnset in most of USofA, so not much use. However, I wanted to check Guide 9's accuracy on that one given the time offset compared to IMCCE for the one early in the UT day. Tried it, couldn't find the Satellites, zoomed out, and found why. They were behind Saturn (at least relative to the Earth). I'll play with it more another day, but as all events here are not due until maybe 2025 (as in mostly daytime ones here until that time) last time I checked, and highly unlikely visually observable, especially in my kit (even Titan transits), the interest for me is more academic.
SUMMARY : IMMCE results tables have a little cog wheel to to top right, press on that and you can select specific satellites or Saturn, toggling them on or off, to customise targets shown in the table.