I don't think you'll regret starting the ball rolling for assessment - it takes a while for appointments to come through anyway. If he has ASD, and he has times when he is managing life well, then great, but good days and bad days, you know what it's like.... and if this is what it is, knowing and getting stuff in place now rather than closer to high school time can only be a good thing.
I didn't as such vacillate - DS1 had always shown signs, IMO, but so far as I was aware at school, he was managing well enough, occasional behavioural issues and socially awkward/inept/immature, which was noticable, and also academically slow/behind, but we always accepted the reasoning that as an August boy he was always going to be a bit on the back foot, so to speak. At home it was always a different story but his dad and I were divorcing and sorting all that out and there were not any crisis points so far as the boys (I have 2 DS) were concerned.
Until a year ago, when it became apparent he was struggling at school. Etc. Behaviour problems escalated, he refuse to do home learning, he claimed he couldn't remember stuff he'd done at school, and a penny suddenly dropped that he wasn't just being purposely difficult, he really could not remember. I arranged a meeting with his teacher (he was 6 and in year 2), which was enlightening to say the least, and I was strongly advised to ask my GP for a referral, which I did. We were all thinking more along the ADHD (inattentive) lines. The referral involved detailed preassessment forms, which I and school completed (again sobering to read their account of him, and there were many - I could see - ASD flags raised by them).
This was a year ago. Last week my son had the assessment and was diagnosed with ASD. It was entirely predictable during the meeting that this would be the outcome and I can barely believe I didn't realise. I mean I knew he was quirkly, difficult, challenging, but he didn't tick some boxes that I thought were really important, such as he seems to have no sensory issues, and I didn't think he had repetitive stuff (though I can see now actually he does, it just isn't the stereotypical hand-flapping).
So it's taken a year. He's 7. And during the year I have second-guessed myself a million times. Is he getting better, perhaps he's just immature? And academically, from really struggling very much, he's turned a corner since going into year 3. He's in intervention classes for maths and literacy and responding to the smaller group situation. He's a smart kid, and the chasm between knowing that and what he was producing/how he behaved in class (basically he was not disruptive but he was in his own world most of the time and constantly needed someone poking him to "bring him back", as they put it). But - I was never going to suggest we didn't have the assessment, even though I wondered. SO glad he's had it now. I don't have the questions or the wondering, it's cleared my head and we can focus on what he needs to get on with life the best he can in a world he doesn't intuitively "get". Nobody is surprised, nobody who knows him, and I am just relieve and happy that it's not up in the air.
THIS is why it's worth going for assessment. Just to know, once and for all, one way or another. Until you do, you'll always wonder.