Search Results: move on from a break up

Hi!

Got "rejected" from my crush after the second date.
She did the classic: I don't know what I want, need to find myself.
But she still wants to remain and hangout as friends.
More or less "Be a nice guy and sit on the back-burner".

She broke up (9yrs rel) with her Ex half a year ago, I guess this also has some toll in her decision.
Oh, just a side-note, it appears they've not moved on from each other coz they're still friends on social-media and liking/hearting each others posts aaand hanging out...

So I did the exit with "I'm not interested in friendship, but if you change your mind and I'm still available, don't hesitate to reconnect".

Now to the topic and question.
Should we remain friends on social media (FB)?
I mean, so I do not completely vanish from the earth.
Maybe someday when she actually are ready and I pop-up as online.. "oh that guy? I do remember him.." (yes, I still have hope in the moment, she did testing the waters for some reason...)

OR

Is this a bad idea, coz then my availability to her won't vanish from earth "enough". Therefor she will have better chance to forget about me, and then maaayybe from a universal coincident gets reminded of me and wants to rekindle?

We live in different cities (1h apart), so chances we bump in each other on daily basis are slim to none, and we haven't DM since two weeks ago, when she did the speech.

Hi there!

Me [35M] work as administrative role in our department, which a new girl[23F], meantime she has her school holidays, began her part-time job just over summer.
Since we're working in a big department, but in separated areas, we're not bumping in each other every hour, maybe except during lunch break, coz we share same canteen. To me she's cute, I'm old.

First encounter
In the beginning of this week, she pops up in my office coz she had some problem with her profile account. So in order for her to show me, she had to logon from my computer, so I moved away a bit to give her space.
After she was done, I rolled back so could start a short troubleshoot on what was going on.
But I noticed something with her behavior.
She didn't back away when I started working (that's what people usually do?), I mean, my office is big and she had plenty of room to casually back off..
So she just stood there very, veery close, like we could with no problem play a game on my computer using same keyboard..
Short after she had to logon again, just to clarify, so I moved away again, but this time "not so far".. So I expected her to try to reach over from where she stood to my keyboard, or just move the keyboard to her so she could easier type.. But nope she went just in front of me and start typing.
Her current position; she could just turn around and sit in my lap... WTF?

And then everything seems good, so she left back to her work.

Second encounter - Coffe machine
We got two machines; I was waiting for mine to be ready and she came and ordered hers.
So I had to ask her if everything is going well now since my high leveled supportexpertise saved her day, and gave her a smirk.
She laughed (giggled?) a bit and said yes, and looked on me very fast and then looked away.
Then I noticed she was super red in her face, blushing (?).. She didn't blush when she was in my office?

Am I overanalyzing things?
Coz now I instead confusing myself and need help.