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I want to say

"I accidentally cast a glance at my watch... shoot! It's 10:30"

except I don't want to use the word "accidentally" (or cast for that matter...). Is there a way to maybe combine them with a word that encompasses both, an unintentional seeing of the time?

My first thought was that you might glimpse your watch:

glimpse

VERB

[WITH OBJECT]

1. 
   

   See or perceive briefly or partially.

   
   
   

   ‘he glimpsed a figure standing in the shade’

   
   

(from the Oxford Dictionaries)

But then I felt that wasn't quite right. What you really did was catch sight of your watch:

catch (or get a) sight of

Glimpse for a moment; suddenly notice.

‘when she caught sight of him she smiled’

So in your sentence, it would be:

I caught sight of my watch... shoot! It's 10:30!

If you didn't intend to look, then you probably wouldn't describe what happened with that verb. (Even if that's what happened.)

You could use one of the following phrases instead:

I became aware of the time.

I suddenly realized the time.

I noticed the time on my watch.

One way to do this would be to take yourself out of the subject position. You can make yourself the passive victim of your watch's attention-getting machinations by using the expression catch someone's eye. From MacMillan Dictionary:

if something catches your eye, you suddenly notice it
There was one painting that caught my eye.

So in your example, you were just minding your own business, not meaning to check the time at all, when suddenly

My watch caught my eye...shoot! It's 10:30!