Mine was just a custom made gray one, but I have seen those red ones, yes :D
I bought bunch of ready made 10 meter cables for lan party dunno 15 or 20 years ago... Used with switch... Grey with nice paper label at end with "Cross over"...
Haven't had any issues with them ever in regular use... So pointless even back then...
If using a switch, there isn't any need for crossover cables, is it?
yes
(, except if you lack an additional power slot or have no switch available)
Mine were grey same as the normal patch cables but had red Hellerman sleeves at the ends.