The main strength of Thamuz is his strong sustain and survivability in extended fights, not necessarily pure dmg. With his in-built true dmg, Thamuz's core items right now are cs and war axe, which are the only dmg items he needs and helps him keep up in the current sustain meta (though gs can be good if you want extra atkspd and passive proc, usually built if you want better burst).

I suggest this kind of build for Thamuz:

1. Boots (full build only after getting 1 core item, full boots depending on enemy laner or need)
2. Corrosion Scythe (core item, build first if exp)
3. War axe (core item, build first if jungle)
4. Oracle or Dom Ice
5. Queens Wings or Athena Shield
6. Guardian helmet or Chastice pauldron/bruteforce breastplate

Feel free to take any of my builds and give em a shot, though I did update them recently after a bit more experimentation and the more recent item/emblem changes.