How much contrast do you want ?
If you engrave first , then stain you will get a darker tone in the engraved part , just because you'll be exposing end grain . Especially with maple . Is that solid , or a veneer on other wood ?
I ask because some of it looks like yellow pine . If it has a maple veneer , one side will be maple , and one side won't , or may not be dependinh on the panel use .
If you want more contrast , you can engave , color the letters , then resand the surface , and apply the stain to that . That's a bit tricky though , and you have to be carful that you don't soak up the darker color on the face to the point you can't sand it out .
You could just stain the whole thing engraved , then go back over the engraved section to deepen the color .
What stain / color are you planing on ? Any finish ? I've been using Watco Danish oil . Makes a nice finish and natural color all in one .
Just depends on what you like , and want it to be . Flat , glossey , or somewhere in between ?
This is Maple with natural tone Danish oil . It's wet , so normally not that glossy .
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This is another with Danish oil . You can see how dark the differnt grain profile gets .
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