There really never was a "SAAB L-12".
The L 12 (or L12, or L.12, or L-12) was developed at ASJA under Erik Wilkensson to replace in-service J 8
Gladiators. The L 12 concept was submitted to the
Flygvapnet which assigned it the
projekt series designation P 9. As the P 9 design firmed up, the
Flygvapnet committed itself, assigning the
jaktflygplan designation J 19. However, by then, the Linköping firm had been merged into Svenska Aeroplan Aktiebolaget. The latter preferred to use
Flygvapnet numbers for types, so the L 12 became the SAAB 19.
Alas, the SAAB 19/J 19 didn't get very far. Another design originating with ASJA - the L 10 aka P 7A - took priority. The P 7A was accepted for service as the B 17 (thereby becoming the SAAB 17) and the J 19 dropped from priority with both SAAB and the
Flygvapnet - which had managed an emergency procurement of Regianne Re.2000s in the meantime.