From any location in Kefa , Gunung Mutis is clearly visible in the distance. In fact, it's possible to go from Kefa directly to Mutis, without passing by Soe. In Eban, 1h from Kefa, Ojeks, the local motorbike taxis, propose the trip to the start of the trek for 100k Rp.
1. Gunung Soep [short]
The West of Kefa town is cut by a large river, uncrossable during rainy season, but used as a road otherwise. An interesting hill very visible from Kefa is Gunung Soep.
If you go on in this direction by following the main river, after 15/20km, you will arrive in the Timorese enclave of Occusi.
It s a 3h excursion from Kefa bus terminal. At the top of Soep, you will find an interesting local sacrifice stone.
By going West from Gunung Soep, you can reach the Kefa-Eban Road.
2. Eban Walk [short]
Numerous Angkot start from Kefa terminal to Eban, 1h30min away, 10k Rp. The route is quite scenic, upon arrival in Eban, there is a fork road, with the left road going to Mutis [or Nuaf Nefomasi on Google Map], and the right road going to a sharp rock outcrop, very visible from Eban, 1km away. The outcrop is populated by monkeys, as elsewhere in Timor, there are not easy to watch are they are hunted for their meat. Locals are very friendly and may invite you for a coffee. The GPS track starts at the beginning of the road from Kefa, and follow the road. The small walk in Eban follows the dust road going up from the centre/main intersection/Angkot stop, I tried to climb the outcrop to no avail, as it is slippery and steep.
3. Gunung Mutis 2407m [long], 5-6h return
Although Eban is the closest large village to Mutis, there's no access from there. For the moment, the only way is to go through Kapan & Fatumnasi [2h/motorbike] by a long, tortuous and bad road. Fatumnasi is very scenic and sports an excellent Guest House: Lopo Mutis Homestay. There's no way you can get lost on the way as there's only one road: from Eban Pasar Baru, turn left, and in Kapan intersection turn right. After Fatumnasi, it's still a 8km tough road to reach the start of the trek, situated near a nice pond filled with lotus & surrounded by high grey cliffs. Don't stop at the man-made small lake after the Forest Office, as it still to far from the start. The forest is splendid, and looks very European.
Don't follow the main dust road winding North down to the village of Punu, a few km away.
From the pond, follow the obvious large path going East, then turning North, there's no way you can get lost until you arrive at a large meadow [1h], with a stream of clean water. Refill, as there's no water afterwards. Cross the swamp and follow the crest northwards with an alternance of meadows and forests, 1h later you will arrive at the foot of Mount Mutis itself and from there it's a 1h hard climb to the 1st summit at 2400m, which has no marking, only some campsite remains, 10min more in the west direction will bring you to the real summit with a cement pillar and an unreadable signboard at 2407m. 2h should be enough to be back to the pond at the start of the trek.
Guido mototaxi in Eban: 081337964463, also provides accommodation at sister's house, very friendly family.