Here is a basic description of inletting an entry thimble. This is just describing the general process. It's not addressing the OP's question in particular. If it's useful, great. If not, ignore it.
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When the thimble is fully inlet the edge of the hole through the tube should be flush with the groove, so that there is no step between the wood and the hole. (If there is a step, then the rod can/will catch on it, rather than entering the hole.)
It's preferable for the flats and the rings on the tube to be very carefully inlet, with wood kept flush against the flats and cut-outs made for the rings, so that there is no gap at the flats. You must cut into the wood at the edge of the groove to inlet the thimble, but you should maintain the height of that wood so that it is the same as the wood in front of the thimble. There shouldn't be a low spot where the thimble sits. You only cut away enough wood for the thimble to drop down into a thimble-sized hole, with wood flush and touching it all around it.
When inlet, the tube of the thimble should be deep enough to be in line with the wood of the groove on one end, and with the wood of the entry hole on the other. Of course, you cannot see the entry hole end (since it's covered by the tab/extension), so this arrangement is checked all through the inletting process by constantly sliding in and out a piece of metal rod equal in diameter to the inside of the tube. (I use a piece of steel rod about 6-8" long that seems to work okay for this. I don't recall exactly how long. Long enough, anyway.) I say equal in diameter to the inside of the tube because this may not be the same size as the end of your ramrod, since many ramrods are tapered. If you only use your ramrod to check this, you can get a false reading. (Most ramrods on 18th c. and early 19th. c. firearms were tapered.)
Of course, there's the tab/extension on the back side of the entry pipe to think about. On the entry pipe you have here, the tab and the tube are integrated, and that means that the whole thing, including the tab, has to descend together. So that means it is not possible to put the tube all the way in first, and only afterward think about the tab. And you cannot just carelessly cut away a bunch of wood at the top of the entry hole while you inlet the tube. You need that wood to be there, as the tab needs to sit down in it. So the tab and tube have to go down at the same time, with the whole thing dropping in at 90 degrees to the axis of the groove and entry hole. (Some entry pipes are made in two pieces, and some people do inlay those in two pieces and solder them together once they are inlet, but that's a separate story.)
As JLayne said, in order to get all this to go in, it's usually necessary to trim the tab. Tabs are usually made a little longer than necessary. On cast or machined thimbles, they may be about the length needed, more or less. When I make them from scratch, I make them at least an extra 1/2" longer than needed, and trim them when the thimble is completed. Trimming them to 1/8" is plenty long/short as a starting point, but even then, if they start hitting the barrel during the inletting process, then they need to be trimmed some more. It's fine for the final length of the tab to touch the barrel when the tube is fully inlet, but it should not be allowed to keep the thimble from descending into proper position, so check it along the way. When installed and pinned, it should not lift the wood away from the barrel. It is normal to inlet tabs with the barrel in place, so that the barrel can provide strength to the thin wood under the tab. Just don't let a long tab hitting the barrel make you think that it cannot go down further. Take the barrel out and check if needed. Trim the tabs as necessary. It is normal for the tabs to be flush with the bottom of the barrel mortise.
If the barrel channel and rod groove were laid out properly, there should be enough room for a pin to go through the tab without having the pin hole break through the edge of the tab or having it break into the hole through the thimble tube. If the tab ends up being very short, then don't be surprised if the pin needs to hit the slope of the tube, rather than just hitting square on the flat. You just don't want the pin hole to come through into the tube. If you think it is going to hit the slope, you can start the hole and mark the slope with the drill, then stop and pull out the thimble, and cut a small flat spot there where drill needs to enter, so that the slope doesn't deflect the drill. (If drilling brass, then it's helpful to use a small hone to carefully change the inside cutting angle of the drill lip, where the flute meets the bevel, so as to make the drill scrape rather than cut. If a drill configured for steel is used in brass, it can cut too aggressively and too fast, sometimes binding and breaking the drill as it exits. Changing this angle helps keep it from going in so aggressively.) Put the drill in and out frequently, to keep it clear. Pins holes are normally not drilled until the very last step, after the entire thimble is fully inlet and the tabs are cut to proper length.
When the whole thing is inlet, then you can take a shop knife or a half-round needle file and carefully cut a very light chamfer around the inside lip of the tube, then polish it with some 400 grit paper. This will help keep the lip from scraping the hickory rod. Also polish the inside of the tube as necessary to be sure there are no rough spots. (If you are making thimbles, then it's normal to do this while making them. But if you are using a thimble that came to you already made, then you may need to do this as a final step.)
Edited: tried to fix typos
