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Does this do want you want?

Cases[Options[i, MetaInformation], 
 HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler because it its Rules all the way down:

Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]

{"ExposureTime" -> 1/65}

All-in-one:

With[{wanted = "ExposureTime"}, 
  wanted /. Cases[Options[i], HoldPattern[wanted -> ___], Infinity]] //
  N

Does this do want you want?

Cases[Options[i, MetaInformation], 
 HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler because it is Rules all the way down:

Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]

{"ExposureTime" -> 1/65}

All-in-one:

With[{wanted = "ExposureTime"}, 
  wanted /. Cases[Options[i], HoldPattern[wanted -> ___], Infinity]] //
  N

Does this do want you want?

Cases[Options[i, MetaInformation], 
 HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler because it its Rules all the way down:

Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]

{"ExposureTime" -> 1/65}

Does this do want you want?

Cases[Options[i, MetaInformation], 
 HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler because it its Rules all the way down:

Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]

{"ExposureTime" -> 1/65}

All-in-one:

With[{wanted = "ExposureTime"}, 
  wanted /. Cases[Options[i], HoldPattern[wanted -> ___], Infinity]] //
  N

Does this do want you want?

Cases[Options[i, MetaInformation], 
 HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler

Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]

{"ExposureTime" -> 1/65}

Does this do want you want?

Cases[Options[i, MetaInformation], 
 HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler because it its Rules all the way down:

Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]

{"ExposureTime" -> 1/65}