I will say here that the Jehovah's Witnesses do get one thing right: the crux/stauros on which a victim could be hung had no definite shape. The T and the † are just two of the forms that a crux could take; the gibbet could be a tree, it could be a simple upright pole, it could be a T, it could be a †, it could be an X.
The Greek equivalent of crux, stauros, comes from the verb ἵστημι (histēmi 'straighten up, stand'), which in turn comes from the Indo-European root *stā- 'to stand, place; upright pole' (cognate with Icelandic staur 'a stake, pole', English stour 'stake, pole'; cf. staff). It originally meant an upright stake or a piece of paling in earlier Greek (Homeric and classical Greek). However, in Koine Greek, stauros also became synonymous with crux, which refers to the gibbet where a criminal is hanged, anything from a simple stake (a tree) to pieces of timber joined together at an angle. One idea has it (could be wrong though) that the word crux properly refers only to an upright stake, but is used as a metonymy for the gibbet as a whole (kind of like how the horizontal beam - patibulum, literally a 'spreader', from patere 'to be (spread) open' - was also at times used to refer to the whole device).
One can't simply argue that stauros/crux only meant 'upright stake' any more than one can argue that it only meant 'T or †-shaped gibbet', because we do have references where T/†-shaped *crux*es are implied.
A Roman citizen of no obscure station, having ordered one of his slaves to be put to death, delivered him to his fellow-slaves to be led away, and in order that his punishment might be witnessed by all, directed them to drag him through the Forum and every other conspicuous part of the city as they whipped him, and that he should go ahead of the procession which the Romans were at that time conducting in honour of the god. The men ordered to lead the slave to his punishment, having stretched out both his arms and fastened them to a piece of wood which extended across his breast and shoulders as far as his wrists, followed him, tearing his naked body with whips.
- Dionysius of Halicarnassus (ca. 60 BC-after 7 BC), Roman Antiquities, VII, 69:1-2
Such are his verbal offences against man; his offences in deed remain. Men weep, and bewail their lot, and curse Cadmus with many curses for introducing Tau (Τ) into the family of letters; they say it was his body that tyrants took for a model, his shape that they imitated, when they set up the erections on which men are crucified. Σταυρός (stauros) the vile engine is called, and it derives its vile name from him. Now, with all these crimes upon him, does he not deserve death, nay, many deaths? For my part I know none bad enough but that supplied by his own shape--that shape which he gave to the gibbet named σταυρός after him by men.
- Pseudo-Lucian (ca. 125-after 180), Trial in the Court of Vowels
Since he is a criminal, he will be crucified in his height and in the extension of his hands.
- Artemidorus (2nd century), Oneirocritica 1:76
Also note the doodle below. This graffito (from around the late 1st-early 2nd century) was found in a taberna located at the vicinity of the Flavian Amphitheater in Pozzuoli (ancient Puteoli). This graffito seems to have been either another representation of the crucified Christ or (more likely) a caricature of a person who was crucified in the nearby ampitheater as part of the brutal entertainment that occurred within its walls.
The sketch shows the victim hanging, arms widespread, on a T-shaped cross. The victim's legs are wide open, with the feet seemingly separate and straddling the vertical beam. Note also the ledge (a sedile?) below the figure's left leg (viewer's right). There is some uncertainty as to whether the drawing portrays the figure as being clothed in a rough tunic or naked, or even whether the figure is that of a man or a woman. (The figure is apparently accompanied by an inscription giving the feminine name "Alcimilla.")
This meanwhile is another graffito, this time found in a house in Pompeii (Insula 13, Regio I). It shows the letters VIV, alongside the drawing of a †-shaped crux, and what looks like a V intersecting with the †. The cross figure could be taken as a rebus for crux. There is some uncertainty as to whether the sketch is a Christian work or not (it could be read as either as the acclamation vivat crux vivat "Long live the cross" or as the insult viva(s in) cruce "may you live on the cross"), or whether the V intersecting with the cross is really a letter or a representation of the sedile.