At its lower end trail 103A connects up with the main trails that cut across the landscape below and to the west of Accellica. The most important of these trails is the 106. You may remember the 106 - it's the same trail that this route started on back near Casa Rocchi. The main idea is to turn right on the 106 and follow it all the way back to the trailhead and your car.
Unfortunately, it isn't quite so simple. There are a lot of side trails in this basin, and it isn't always clear which trail is the main trail 106. There are some big information signs with large map displays in several spots around here, but again where you are on the map isn't always clearly noted - so you are left guessing about your exact context.
A couple of hints to keep you on track: 1) follow the 106 in the direction of Varco del Pistone, 2) follow the signs to the Grotta dello Scalandrone, and 3) follow the Sentiero Italia (which twins with the 106, all the way to and beyond your trailhead).
All of the Picentini Mountains are composed of very soluable limestone and marble, and so caves and holes and such are common. A particularly big and well-known cave in the area is the Grotta della Scalandrone, and it is apparently a fairly popular destination. As a result, the trailwork and infrastructure around the cave is much more "front country" than some of the other stuff encountered so far on this loop. And if you have a headlight and the time, a pop-in to the cave might be worth while. I believe there is an underground river and pond in there, among other things.
If you make it to the entrance to the cave, you are on the right track. Continue beyond the cave and follow not-well marked paths generally downstream. You will have to ford the stream at least once. You continue, ignoring unmarked side paths, until you get to the obvious and well-signed 106/106A junction (and you also see one or two big Sentiero Italia signs). When you get to this junction turn right, staying on the 106 (do not take 106A).
From here things get simpler. Follow the 106, which is clear but at times faint, as it winds up and down and across the low ridges and valleys below Accellica. If in doubt about whether you are off trail, just go back to the last obvious bit of path or trail marker. There were one or two spots where I got a bit off track, but searching around soon revealed a red/white marker that was hidden behind a few leaves or a bush or something. As you approach the Varco del Pistone, the trail more obviously is following the bed of a really old road. And then you'll look up and see the distinctive white rock-cut from the start of your hike. Walk up to and through the rock cut. At this point the loop portion of the route is finished.
At the Varco del Pistone, turn right and follow the forest road back to your car. When I did this route, I took probably an extra hour or so doing necessary bits of routefinding, and completed the whole thing in just over eleven and a half hours. Knowing where you're going and perhaps upping the speed a little (and perhaps parking a little closer to the Varco del Pistone), this loop should be easily doable in ten hours. I myself will definitely have to do it again when the clouds/weather are more favorable. I'm sure I missed out on a ton of great views.
And finally, here is a short video sequence from the start of the hike to the main (North) summit.
Monte Accellica Climb - Video