Sometimes when I haven't studied go a lot, but have been actively studying another topic, I'll play a game to relax.

It could be a coincidence, but I get the feeling that, when I am "studying well" in a non-go related area, I also play go better, even though I have not been explicitly studying it. Does anyone else share this experience?

It might just be my imagination...

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be immersed

I find that happens even if I haven't 'studied' other things. I think it's because you consolidate what you've gained when you sleep and rest. If the period is too long, however, decay will happen instead. But a good period of rest is often helpful.

I agree with nyuubi. It takes time for things to sink in, so one needs to take breaks now and then. Be it either by going through a phase of playing rather than studying or doing something completely unrelated to go. Even at my low, low level this is true I've found.

I can be a bit too results-oriented, so when I've been studying something strenuously my attempts to apply what I've learned are laced with anxiety to prove to myself that I'm improving. This is one thought too many. When I haven't seriously studied Go for a week or two, I'm a bit duller and my play is probably a bit lax, but I am purely focused on playing and having fun.

In an interview the late Hans Pietsch stated that his teacher could immediately see if he made his laundry this week or if he cleaned his appartment, because if he didn't these unresolved tasks somehow haunted him in the back of his mind and he could not play to his fullest potential.
He also says that quite a few professional Go players have a strict daily schedule to be able to be focussed when they play Go.

I found that - at least partly - to be true. If I should study other things and play Go to distract me from it, I play worse. Or if I solve Tsumegos instead of learning for a test, I get really hasty after a while, not able to focus to read through a whole sequence.

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My "guide" to become stronger in Go

It makes sense to me. When you are studying well your mind is in a good state for playing go. Every game is a learning opportunity. Faced with a position for which you do not know the right play, you have the opportunity to learn what it is. This is not rote study, but the application of active intelligence.

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The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Maybe it was the smell that was emanating from his direction?

I don't think there is much overlap between alternate study and doing well at go. However, when you are on top of your game you are on top of your game. There has been scientific evidence that one can increase ones working memory via training albeit slowly, so maybe there is a connection. Then again some people seem to play better with a beer in their hand.

I find that often, whatever the subject I'm studying is, I do it better after not doing it at all for a while. This includes go. I think it's because you not only rest and let all that you learned sink in during that time, but you also come into the game with a new perspective. I stopped playing for a week, and when I started playing again, I was surprised with a lot of the moves I played because they would have seemed like nonsense and I wouldn't even consider them a week ago. I guess it also has to do with habits: playing others, you pick up certain habits that need time to go away, and they do after a little break.