Dating

Is it normal for a guy to take his time on dates and getting to know me or is he emotionally unavailable?

I work with this guy whom we recently hung out and went to dinner. He asked, and We didn’t call it a date but everything he did that night screamed date; picking me up, paying for dinner, opening the car door for me, letting me borrow his jacket; hanging out for over 3 hours. He even invited me to his new year plans.
He texted me the next day, and when we saw each other at work we were cool and ourselves around each other. It’s always hard at work bc you never know how you’re supposed to act so we’re jokey and flirty but not obvious.
I couldn’t go to the new years thing bc of an obligation but he texted me that night and said happy new years I’m not sure what this new year brings but let’s grab dinner again sometime soon.
When we saw each other the next day, he brought up the dinner but never set a day, so I asked what day were you thinking? I was expecting him to say one of our days off that week but instead he said maybe sometime next week. Again didn’t set a day. But I was like maybe he’s got a busy schedule.
Normally these look like good signs of interest but I feel slight caution with some things he does. For starters he asked the day of if I wanted to go out, and lucky for him I was free and went for it. Also whenever I see him at work it’s hot and cold. Some days I feel he’s all in, close by me, making effort. Other days I could feel him keeping distance. And when no one is around that’s when he’s himself and shows interest. I’m nervous he’s gonna pull the same thing and ask to hang the day of, and for me personally that makes me think he’s not taking me seriously..

But also, is that normal behavior? Like not trying to rush this but still puts in effort? Maybe not as quick and persistent, but he’s showing interest and effort.. how would you take this situation?

Is it normal for a guy to take his time on dates and getting to know me or is he emotionally unavailable?
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