Activate voice control through Bluetooth headset

Re: "Activate voice control through Bluetooth headset. Is there way to make voice control respond to voice input

from my Bluetooth headset? It seems that it only responds to the internal iPhone mic"

Am no expert in this area, yet your request deserves some response. A few settings suggestions follow below.

Else: For more expert support: see the link underneath:

If you haven't already tried them, wondering if the settings below can help:

Try Settings > Sound and Haptics > Microphone >

If headset is not listed: You may have a choice of Internal Microphone,

External Microphone,

or Built-in Microphone)

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If needed: for using headset for Phone calls:

Try Settings > Accessibility > Touch > Call Audio routing >

Choose from Automatic,

Bluetooth Headset, or

Speaker.

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For expert support with using Voice Control: You may want to reach out Apple's Accessibility Support Team:

How to contact Apple for help with accessibility features - Apple Support

or

Apple's Accessibility Support Website

(NB: You can "Get Support" (online chat / phone / email etc.) from the link at the bottom of their website:)

Accessibility Support - Official Apple Support