That looks like perhaps someone was over-enthusiastic lubing the selector mechanism. There are seals on the shift rods and they frequently do leak; but they are slightly farther forward..
Changing those seals can be a bit tricky. First you have to remove the shafts, which means you have to get out the square head taper pins that hold the shift forks on the shafts. The early ones with the safety wire usually come out with the help of some appropriate tools (an 8-point socket, extension and a T-bar handle so you can turn from both sides and avoid any side force on the pin). But later ones have a self-locking insert and frequently break at the insert. I don't know offhand when the change was, but the TR4 manual doesn't mention the safety wire so I'm guessing early TR4 had the self-locking pins. Looks like Moss has the pins (though they call them setscrews) for only $14/each.
It's possible things have changed, but last time I ordered those seals, what I got were ordinary O-rings that did not fit the cavity very well. I bought some Teflon "backing rings" from MMC to fill the gap and make the O-rings fit snugly. I also bought "quadseal" O-rings from them, which was probably overkill.
The other fun part was reassembling the shift interlock, which is quite important to proper operation. The center shaft has a pin through it, then there is a ball bearing on each side between the pin and the adjacent shaft. I held the pin with some heavy grease, installed the center shaft and pin; then held the cover sideways and rolled one ball down the bore until it fell into it's hole so I could install the shaft on that side. Then flip it over the other way and do the other shaft. Check carefully that the interlock works as it should (both other shafts lock if any one shaft is out of neutral); as it is easy for the ball to fall into the wrong place or get dislodged when you insert the shaft.
Might as well check the detent force while you are in there. I used a cheap digital fish scale, which worked OK but required steady hands to get a reading just before the shaft moved. Might be easier with either a more expensive digital scale; or an analog one, so you get a reading instantly instead of having to wait.
It pretty much only goes together one way, but lots of photos are a good idea anyway. The shafts and forks are all different and they obviously have to go in the right position (and turned the right way) or it isn't going to work.