Nope, it's (again) my bad. The current implementation of the encapsulated version "assumes" (falsely, obviously) that the state's base tax-rate is baked into the local sales tax rates.
An update is forthcoming.
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I think that the local taxes are not applied for store pickup orders. When notify_order_cart_external_tax_rate_lookup() is called, $taxZoneId is the shipping address zone_id, not the store's zone_id. I do have "Store Pickup Tax Basis" in the local sales tax config set to the zone of the store.
I have posted a possible fix in the repo for this plugin's Issues section.
v3.0.1 of "Local Sales Tax" is now available for download: https://www.zen-cart.com/downloads.php?do=file&id=422
This release contains changes associated with these GitHub issues:
#5: Include state's base tax-rate in the local sales tax.
#6: Correct previous plugin removal; the base admin tool's name was local_sales_taxes.php.
#8: Incorrect tax-rate charged for storepickup orders.