Interestingly enough, the non-state-highway gap in 39 was actually signed from about 1958 to the mid-70's -- with older porcelain-white button-copy 1955-type shields -- in fact signage indicating route continuity was at least as complete, if not more so, than other urban state highways in District 7. Los Angeles County maintained the signage, with at least the tacit complicity of the Division of Highways, who likely supplied the shields themselves.
North to south, the route was signed from the I-10/Azusa Ave. interchange, using South Garvey Avenue (the south I-10 frontage road) west from Azusa immediately south of the interchange. It was signed west right along the frontage road to Hacienda Blvd., where it turned southwest. It continued on Hacienda Blvd. south through West Covina, La Puente, and Hacienda Heights before going over the top of the Puente Hills. The Hacienda Blvd./quasi-SSR 39 alignment continued to Whittier Blvd., where it turned west to Beach Blvd. The full signage of this section lasted until the 1964 renumbering, when state highway shields were changed to white-on-green.
After 1964, the county apparently lost interest in signage of this route; the black-on-white shields disappeared along the South Garvey frontage road, and were seen only sporadically along Hacienda. Curiously, when the CA 60/Pomona Freeway was completed through Hacienda Heights in late 1967, the Hacienda Blvd. exit signage showed that street as CA 39. When CA 72 was signed on Whittier Blvd and Harbor Blvd. in La Habra in 1968, the junction with Hacienda Blvd. clearly indicated that route as CA 39, complete with new green shields. However, Hacienda Blvd. itself remained sporadically signed, even immediately north and south of the CA 60 freeway. After 1964, there was no signage on southbound CA 39 to indicate that it continued south of I-10; northbound, the signage simply "petered out" north of Francisquito Avenue in West Covina. The expansion of the Westfield West Covina mall in the 1970's, which included a reconfiguration of Hacienda Blvd. that moved the main flow of traffic to Vincent Ave. west of the mall and the downgrading of Hacienda Ave. from Vincent north to South Garvey to more or less an access road to the east side of the mall essentially put a nail in the CA 39 signage "coffin". By 1982, a "TO" banner was placed on the CA 60 BGS reference to CA 39; a few years later, the shield was greened out completely.
In the early 2000's there was one "straggler" green CA 39 shield on NB Hacienda north of Anza; it was gone by 2010, the last time I used that street. With the north end of Hacienda Blvd. essentially a mall access road, and South Garvey having been truncated when the I-10/Azusa Ave. interchange was reworked in the '80's, there is no current physical continuity along the original L.A. County-signed route. Hacienda Blvd. through the Puente Hills remains a twisting, curvy 2-lane road -- albeit well-delineated with Caltrans-type outer lane striping.
Both the Harbor Blvd./Azusa Ave. corridor from east La Habra north to Covina -- the route described in the CA 39 legislative description -- and Colima Ave (county N8) crossing the hills to the west are multilane boulevards, but they certainly don't look like Caltrans-spec facilities (short left-turn pockets, curbs rather than shoulders), rather typical arterials through the housing tracts that line the Puente Hills. My assesment is, and has been for some time now, that despite the state legislative description, none of the relevant jurisdictions have any interest in signing and maintaining any surface connection between northern Orange County and the east San Gabriel Valley. IMHO, they may as well relinquish any vestiges of CA 39 north of Whittier Blvd. Locals already know how to get up to the San Gabriel Canyon; tourists with GPS will find their way up there as well (and others just need to ask!). Keep the canyon section signed, sign it as something else north of I-210, but forget anything south of there to La Habra. Further south, Beach Blvd's identity as "Highway 39" is as longstanding as the modern existence of the region; it's appropriate, for navigational purposes, that such signage remains undisturbed. But it's patently obvious that Caltrans wants and intends to shed as much surface-street mileage as it can; adding more just isn't in the cards.