To shine on something
Back to the example of the flashlight - if you "shine a flashlight on something" - you already suspect we are not going to use "זֹהַר", right? Right! :)
Because when we "shine on something" the purpose really is to shed light on something, in order to see it better.
So - light - how do we say "light" in Hebrew? Like in "let there be light." :) Right, - it's אור.
There is a verb derived from this this root - להאיר. And this is exactly how we would say "shine a flashlight on" - לְהָאִיר עִם פָּנָס
Another example -
"The lamp lights up the room with a soft light"
הַמְּנוֹרָה מְאִירָה אֶת הַחֶדֶר בְּאוֹר רַךְ.
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And of course, this word, too, is also good for making names - remember Golda Meir? ;) If not - you are welcome to Google who this interesting women was. :)