Here's some words to do with chariots and whether they suggest proper Celtic light, two-wheeled ones like excavated British chariots or heavy, four wheeled carts, taken from eDIL:

carpat means a chariot. It also means a cart or wagon. Which came first?
á - is another word for a chariot. An ara is a charioteer and araidecht is chariot driving.
There are two Irish words for horse; capall is a draught horse, ech is a riding horse. A chariot is drawn by the ech, not the capall, which suggests it's not just a cart for transportation.
cethairríad means a four-wheeled chariot, or possibly a four horsed chariot. Does this mean by default all others are two-wheelers?
cis is part of a chariot, which is glossed in the Táin as meaning the same as fonnad.
clangdírech is another word for a chariot.
clár means any flat thing made of wood, and is used to refer to part of a chariot (in modern Irish it's used for the table of contents in book)
crett is translated as frame, body or trunk.
dériad is translated at "two horse chariot" but why not "two wheeled chariot"?
faitse means the right or the south side, or the charioteer's side, as opposed to the fochla, the north or warrior's side. It's hard to get two men side by side in a British chariot because of its size, the charioteer and the warrior are positioned diagonally, but they could still have customary sides.
féthan is given as "some attachment of a spear shaft, scabbard or chariot pole, generally made of metal"
fidgrind - yet another word for a chariot.
focharpart is some other part of a frame of a chariot.
fogaimen is a rug which goes in the chariot; same as a forgemen which goes with a fortche.
fonnad is a word which has a really long entry in eDIL. What it means seems to be the iron tyres that go round the wheels. This ties in with British chariots.
frithbacán is a hook used to stop a chariot when not in use. Is that significant?
noíglinne is a frame of a chariot - the first element suggest nine of something.
síthbe means a chariot pole.
tarbchlár (bull(hide)-clár) is another panel-like part of a chariot
ucht is translated as "front panel of a chariot" - a British chariot doesn't seem to have one.