Hello, welcome to the site :-)
I can remember my LO lying awake doing the 'seven mile stare' for ages when he was that age, just like yours. I left him to it, as long as he was content I left him. At that time he was having day naps in the living room so I was in and out keeping an eye on him, usually he'd eventually nod off on his own and I thought that was great, truly independent and no crying or fussing. Sometimes he would stare like that for a long time and then have a little fuss, I tended to do as little as possible, eg say 'it's ok mummy's still here' or 'it's ok you're just tired, off to sleep now.' If the fussing escalated I'd do a little shush pat. Escalated more I'd sing him a song he knew, more and I'd pick up until calm then put down. To be honest I didn't keep track then of exactly how long he slept because it never seemed to be an issue, I just followed his cues.