Not much background though

I don't know if this counts as a rare vehicle but...
http://imcdb.org/vehicle_1721065-Easy-Rider-M50-2003.html
One issue, the country origin is unknown

Found it - 1957 Jaguar Mk.VIII Spohn Coupé. Not really an Alpine lane ...

I'd count this M5 wagon
https://imcdb.org/vehicle_1946984-BMW-M5-Touring-E34-1992.html

This convertible from 13 Going on 30
https://www.imcdb.org/vehicle_777564-Crayford-Mercedes-Benz-280-CE-Cabriolet-W123-1978.html

Of course this Weidner

http://www.imcdb.org/vehicle_1327686-Weidner-70-S-1957.html

the only Manderbach

http://www.imcdb.org/vehicle_1274501-Manderbach-Kleinlastwagen-1949.html

Glas 3000 V8

http://www.imcdb.org/vehicle_1299022-Glas-3000-V8-Coup%C3%A9-1967.html

This -still listed as unknown- Colombian R4 derivate

http://www.imcdb.org/vehicle_118582.html

Sungri Paektusan

http://www.imcdb.org/vehicles.php?make=Sungri&model=Paektusan

The only random Zündapp Janus on the site - and even in USA

http://www.imcdb.org/vehicle_1370383-Z%C3%BCndapp-Janus-1957.html

the only random German made AMC Javellin

http://www.imcdb.org/vehicle_1051467-AMC-Javelin-79-K-1969.html

the only Trekka

http://www.imcdb.org/vehicle_1588829-Trekka-4-16-1971.html

the only background MAVA-Renault Farmer

http://www.imcdb.org/vehicle_910165-MAVA-Renault-Farma-1983.html

the only random Rom Carmel

http://www.imcdb.org/vehicle_573287-Rom-Carmel-1301-1979.html

Autocars Sabra Sport made for S

http://www.imcdb.org/vehicle_205306-Autocars-Sabra-Sport-1965.html

NSU Prinz 4 made in Chile

http://www.imcdb.org/vehicle_228968-NSU-Prinz-4-Typ-47-1962.html

Chevrolet Royale

http://www.imcdb.org/vehicle_248951-Chevrolet-Royale-1974.html

Still no AWS Shopper on the site - but something else very rare from annother same-named company

http://www.imcdb.org/vehicles.php?make=AWS&model=


We have 8 Iso Rivolta GT listed - but only one on a junkyard

http://www.imcdb.org/vehicle_200954-Iso-Rivolta-IR-300-GT-1965.html


Sorry @dsl, still no made for DDR Hillman Minx on the site, this is the only made for DDR vehicle from Britain:

http://www.imcdb.org/vehicle_881969-Leyland-Beaver-LAD-1965.html

https://www.imcdb.org/v613647.html
Another 1-off random background. Well known car valued at multiple millions now. Not so much in 1969.

... and Steve McQueen's customised Mini Cooper S is probably worth a ping.

Two nominations - not very exotic, but definitely quirky:
- Austin A35 Pickup in the real world
- enigmatic Commer Express 4-door Estate in India. No obvious explanation for who/how.

Another which I can picture but not remember the details - it was a traditional Brit 50s thing (Jag? Bentley?) convertible with German/Austrian/Swiss body in a late 50s Swiss/Austrian colour film parked in traffic along an Alpine lane on a sunny summer day. Body might have been a name something like Spion - there was some chatter on the page about what/who until it was solved.

Sorry, indeed I missed the point

As rare background car, we have this Citroën GS Birotor:
https://www.imcdb.org/vehicle_927850-Citro%C3%ABn-GS-Birotor-GZ-1974.html
(one of 847, and not many survived)
The related Citroën M35 only occurred in "on purpose" background cars, that does not count I guess