is the [Account Status] field a look up field? if so, then you should probably create a pipeline/webhook/ or perhaps a button that the user click to change the status to Signed Customer on the parent and also stamp the date/time on the child.
if it's on the same table, then while you can still use pipeline/webhook for it, easiest is probably a dynamic form rule that stamps a field of the date/time when the [Account Status] has changed to "Signed Customer". My method of choice would be a button to change the status and also stamp the record
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Tim D
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