VERY FEW people have seen Ginyu’s true form, due to it being abandoned so long ago. He had been a teenager when he had done this, just about fifteen years before his involvement with anything related to the PTO. It isn’t much of secrecy as it is Ginyu feeling that it has no real significance. The loss of his true form doesn’t mean all too much to him, and he rarely holds onto physical sentiments such as photographs, as to him, those sorts of things are easily lost. And less of a headcanon but a small reminder: Salza is one of few people who had seen this form.
Technically, Ginyu IS immortal, as he is more of a spirit, or perhaps even a parasite who is capable of taking bodies that are younger than himself. The only real way to kill him is to kill the body he is inhabiting, before he is able to change.
Ginyu LOVES being a leader, and is often assigned to new recruits in his downtime when the Ginyu Force’s skills are unneeded, giving him the opportunity to train others. His training is tough– but he tends to be extremely encouraging.
Despite his optimism, Ginyu can be ruthless to those who cross him, even going as far as to kill underlings that speak against him, though with those he is close to, he usually just resorts to scolding.
I’m not saying he has considered swapping into Frieza’s body, but he totally has.