Using Search Builder to search on a field with custom location gives DB error
For completeness, my comment probably should have been an answer…

I think this is probably a bug. 

It doesn't matter if you create a new location type or use a pre-populated one. The sql has a column that doesn't exists and it's going against the wrong table. 
Here's the sql: 

SELECT DISTINCT UPPER(LEFT(contact_a.sort_name, 1)) as sort_name 
FROM   civicrm_contact contact_a 
WHERE  ( ( LOWER(Home-location_type.name) = '8' ) ) 
AND    (contact_a.is_deleted = 0) GROUP BY contact_a.id 
ORDER BY UPPER(LEFT(contact_a.sort_name, 1)) asc 


[nativecode=1054 ** Unknown column 'Home-location_type.name' in 'where clause'" 

AlanGallery submitted a bug see comment above.