Based on personal experience and some stack overflow searching, I don't think Android provides any APIs for showing a down arrow instead of the system back arrow. Ted, are you aware of any APIs that allow this?

Correct it seems like it's infeasible (at least without some rather gnarly hacks) according to: https://stackoverflow.com/questions/38892350/how-to-change-android-back-arrow-to-down-arrow

Marking as WontFix unless we have another solutions.

Yeah, I'm not familiar with any APIs, so WontFix seems right to me (although we could reach out to the gboard team internally to see if there were any options, but I doubt there are).

Maybe the Android and Gboard team should be asked what they can do because surely there are many scenarios where developers would like the system back button to point down, especially with controls starting to move to the bottom of the screen in apps (which is the new guideline recommendations if I'm not mistaken). I doubt Chrome Home is the only scenario where this would be useful 

Android also has an open source form for reporting bugs if you would like to file a feature request: https://source.android.com/source/report-bugs

Note that some OEMs customize the system buttons. Many Samsung devices, for example, have a hardware back button that lights up.

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Thank you. I'll do it but isn't it more likely to be taken seriously if someone from within Google were to request it? 

Hmm.. I forgot about hardware buttons. We should try both paths but I'll see if anyone on the Android team has thoughts on this. 

I filed it in case anyone is interested https://issuetracker.google.com/issues/62685916

Thanks for filing. I starred it so that I can follow along.