The Sales Pricelist's field name is actually property_product_pricelist, which indicates it is a field of type property (deprecated in v8).

Basically, the values for this field are not stored in the res_partner table as I expected.

Each record is stored in the ir.property table, as you can see if you view the database with the following query:

SELECT * FROM ir_property WHERE name = 'property_product_pricelist';

You can theoretically update the values by SQL commands, but I would recommend against it (maybe someone else has a good way of doing that safely?).

For some better understanding of property fields, check the following links:

V6 Documentation: https://doc.odoo.com/6.0/developer/2_5_Objects_Fields_Methods/field_type/

Beginner question about functional fields and property fields?: https://www.odoo.com/fr_FR/forum/aide-1/question/beginner-question-about-functional-fields-and-property-fields-77398#answer_77401

Can anyone clearly explain property fields?: https://www.odoo.com/fr_FR/forum/aide-1/question/can-anyone-clearly-explain-property-fields-42887