I think it's possible to trade the indexes intraday. In my data, the percentage of days where you gap (close -> open) less than 1% AND close more than 1% is about 14%. So that is, for those days that do not gap appreciably, the chances that the close is 1% away from the open is about 14%. Say that it is wrong and is actually 20%. Can you build a strategy around this? Can you "characterize" the first few hours/minutes of the trading day for such days? They have a character for sure. I bet you can probably find relationships between overnight trading and regular trading hours as well but I don't trade futures so I haven't bothered to look.
I'm not saying I have been successfully doing this for eons but this is how I develop my index-related strategies. It's really, really boring to execute but there are a ton of situations you can think of and develop strategies around those.
Let's say (for example) you find some set of logical conditions under which you can say 85% of the last 5 years of such conditions have resulted in a trade that nets you 0.1% per day. That's not a bad return. Then repeat, repeat, repeat and size such that you don't lose an entire year's worth of gains in one day. This is where "characterizing" the day comes in handy. Let me not tell you about the time I "eagerly" characterized the day and went in for 100 contracts the wrong way.
If you get bored doing nothing all day like me, then just keep developing more strategies and trying out new things. You can repeat the above pattern for any time frame you like, and it probably also applies for rate futures.