Since we started working remotely, engaging in meetings is harder. I don't have the same feelings that I have when someone is in front of me. It might be the lack of eye contact, not being in the same room and many other factors. That said, goals are achieved, code is committed and Job gets done. The tradeoffs of remote working are there and at the same time, the small things that are different and don't get me to fully engage can be in part attributed to the setup and what that sparks on me.
Naturally, being a host of the meeting requires you to be very active and vigilant of what's happening around you. As a host, you are doing your best to juggle multiple things at the same time such as asking questions, leading the meeting, getting to achieve the intended goal. You can, of course, do a terrible job if you don't care about it and you are put into this position but even when that's the case, you'll be at a different "activation" level in comparison to when you are not the host.
There are multiple elements that will estimulate you to be engaged as a host:
Whenever I am invited to a meeting and I accept, I am declaring that I am interested in it. Interest alone is not something that should drive my decision but it does. I many times leave the decision of if I would add value or not to the organizer of the event which is sometimes not correct.
Let's say I have accepted the meeting and I am now in it. It is my Job as a participant to be familiar with what is going to be discussed but in my experience I am not that good at doing pre-meeting work.
A well defined agenda will allow you to be more critical to which part of the meeting you are more likely to bring some arguments and give you an easier yes.
I also think that many times I have FOMO when a meeting is more informational and in that sense uni-directional. Some people can multi-task and use time of the meeting to do some "deep" work while having 10% of their attention on the subject. That doesn't work for me. I am extremely single-task focus. This strategy does not work for me. I am so much more mediocre when I multi-task that I stopped trying a long time ago. Watching later on a recorded version or reading an email with some bullet points should be enough.
What has been working for me lately is taking notes. I type alone brief sentences of what are the question, answers and points brought in a meeting. This helped me tons getting very quickly into the topics on discussion.
At some point, I even get so engaged that I can't help myself and asking tons of questions, and before I notice I switch from a passive participant (actively taking notes though) to an active member of the meeting (to the perspective of others).
Again, I can't talk and take notes at the same time but I can talk and later on summarize.
So to make it very clear after all that rambling. What helps me engaging as a participant:
I am more likely to be engaged to a meeting if I am the host. Sometimes that is not possible and many times I don't even want that. If you are the participant make sure you can add value before going to a meeting. It helps me a lot taking notes, it might help you to.