When Tegan is saying goodbye, she is saying goodbye to the Doctor first. He’s in the light, he’s always been present as ‘the light in the darkness.’ Which is a good hint at enlightenment during this scene where Tegan is firmly deciding to leave them both. During Tegan’s last episode, she unfortunately doesn’t get to do much. The important part is when Turlough reunites with her after he went missing. He even says:
‘She’s a friend.’
He says it right to her. In front of her. And this time she doesn’t protest like in terminus when asked if they were friends she responded with:
‘Not yet.’
But in her last moments they are now officially friends. Although, in the last scene she shares with Turlough, Turlough has regressed to cowardice with being inaccurately educated in how the Dalek virus works. He’s preserving his safety just in case.
That’s Tegan’s last impression of him. Which is why it’s so shocking to him and us as an audience tha she shakes his hand. Turlough is hidden in the dark - yet again contrasting to the Doctor who is in the light. Which is, the guardian comparison. Yet it’s how we view Turlough, in the dark. Yet when she says his name, he scampers towards the light to shake her hand, almost as if that’s his desperate attempt to seem like he’s a good guy after all. He doesn’t expect anything from Tegan, but their friendship was so hidden between themselves that they were surprised to even get to say goodbye like that. Especially since they never got a proper introduction