A few thoughts:

One, could you consider playing a song for her that has some sort of meaning to you? My therapist was weird about this idea at first, and I only did it once, but playing the song (from my phone), then talking about it felt connecting.

You mention not wanting her to look at you when you're talking about trauma, how you sit turned away much of the time. You also mention how she asked if something you needed was her closing her eyes. I have no idea if this could help or not, but what if she kept her eyes closed for a bit while you faced her (you could both be talking or being quiet). Then, you'd see her, but she wouldn't be looking at you.

One way that I connect with my therapist is talking briefly about "non-therapy" things. Like maybe we're talking for a minute about a TV show or a local sports team or a hawk we just saw outside. Not sure if you do any of that already, but spending a couple minutes at the start or the end on that could potentially be helpful.

What you mention about the scarf--that seems like a way for her to remind you she's there. If you're both holding onto it and need a reminder she's there, maybe you could pull on it, and she could pull back? Or could you come up with some sort of nonverbal/nonvisual signal that you want to be reminded she's there, like two taps on the couch, then she can do two taps back (if that would make a sound) or tap your foot on the floor, she taps back, something like that?