Can I have a text entry customer-lookup and a related-customer drop-down in the same table regarding the same relationship?

It sounds like you want users to be able to directly key the account number if they know it, or else look it up using a drop down list (if they have Admin Permission level) 

No problem,

Make a formula numeric field for the reference field on the relationship as the final relationship.

So you will have your existing relationship, but do not pull any lookup fields (nor make any summary fields) from that Relationship.

Then make a new relatioonship and for tyhe rerfence field on the right hand side use a fomrmula field like

IF([Account # (direct entry)] >0, [Account # (direct entry)], [Related Account #])

ie have a formula to use either the direct keyed account or the lookup account from the drop down list.

Make a formula numeric field for the reference field on the relationship as the final relationship."
Am I creating a second relationship?

Yes a 2nd relationship which will be the one that you will use for any lookup fields or summary fields.

Bare with me... The new field should be created on the Parent or Child table, and I enter the code after the relationship is created?

no problem, I often rush with my answers so they are not as detailed as they could be.

The new field will be on the child side.  Make the new formula field first field first and it would look something like this

IF([Account # (direct entry)] >0, [Account # (direct entry)], [Related Account #])

but I don't know what your fields names actually are or if that field account # field is numeric or text .....


Then make the 2nd relationship, but rather than letting Quick Base make a new field for you called [Related Account], use the formula field.

So I changed it to a text formula field, and I must not be assigning the correct fields to the formula, or making the correct selects for the Proxy field, because all that is appearing is the field name.

It's actually just mirroring what I enter in the 'Enter Account #' field rather than giving me an option to search through accounts.

You will have two fields on the form.

The first field will be the direct entry of the account number.

The 2nd field on the form will be the usual field with the drop down list just like you would have normally done that.  So the user can decide which to use or you may chose to control that with form rules.

Do you have two relationships?

Can you tell me the name of the field for the reference field on the right side of each of the two relationships, and tell me the formula for the one that is the formula field?

Account # For Relationship and Lookup Customer