... I have not been able to trace Elizabeth Standbridge-Terry in the United States of America either.
I didn't find her either at ancestry.com. As I write this, I realize I didn't try familysearch. I will later today. familysearch.org is a good site for US records and is free. It just requires setting up an account. But the early 1800's is very early to find any records available.
There may be county histories or histories of early Harrisburg online. You will need to google for them, as they could be anywhere. Some counties have good genweb sites, where county resources are available or at least pointed to. And there used to be some freepages on rootsweb; it was offline for a while, but some people may have restored their information.
Harrisburg is in Dauphin County. look for that as well. Records in the US, outside of New England, are kept at the county, and Genweb was organized by county.
Researchers often think in terms of the county.
I'm not sure if this will help:
https://www.deathindexes.com/pennsylvania/index.htmlAnd some people are firm believers in Cyndi's List website of genealogy resources. I probably should look at it more often myself.
Try googling 'Dauphin County genealogy resources' or similar.
Is there a local county or city Genealogy Society? Or can the local library in Harrisburg help, at least to point you in the right direction? Their site might have a Genealogy Research section.
Look for the "random acts of genealogical kindness" website. I think it was
continued by someone else when its original maintainer died. They are known for doing voluntary lookups, but someone local to Harrisburg might be able to help.
Last resort, hire a local researcher, but where to get a recommendation is another question.