The location is still(!) listed in MOVE app at this time.
I finally found a picture of this location, and I must have seen it before, because it's right there in the BKW document explaining how mobi-charge works https://www.bkw.ch/fileadmin/user_upload/e1_20855_PB_Mobile_E-Ladestation_mobi-charge.pdf
We see the charger was indeed in the public parking lot, in the row closest to the castle wall, near the parking meter. There were attached T2 cables for both sides. We don't see what kind of signage was installed.
The document and picture are not dated, but it's presumably from 2021 since it mentions "next year 2022".
The text about Aarberg mentions it was a 6-months evaluation period:
Um die Bedürfnisse der Bevölkerung hinsichtlich öffentlichen Ladestationen für Elektrofahrzeuge zu klären, setzt die Stadt Aarberg unsere mobile Ladestation ein. Damit gehört Aarberg zu den ersten vier Gemeinden im Kanton Bern, die so während sechs Monaten zukunftsweisende Erfahrungen für eine E-Mobilitätsstrategie sammeln.
There actually a second document, in French only https://www.bkw.ch/fileadmin/user_upload/01_Infrastruktur/01_01_Bau_Betrieb/Netzinfrastruktur/Netz-_und_Anlagebau/E-Ladestationen/e6_20950-T01_Sonderaktion_E-Mobilitaet_fr.pdf
Aarberg n’est qu’une des quatre communes à avoir réalisé ce test pratique de six mois en 2021. La station de recharge mobile mobi-charge a été mise à la disposition de la population sur deux sites. Cette dernière en a fait un usage intensif. D’après le conseiller municipal Hans Käser «… bien avant la fin de la phase de test, il était clair qu’Aarberg avait besoin d’une borne de recharge électrique publique. Celle-ci a rencontré un écho positif auprès des utilisatrices et utilisateurs …» La coopération entre la commune d’Aarberg, l’entreprise d’approvisionnement en énergie EWA et BKW Power Grid en sa qualité d’entreprise intégrée se poursuivra en 2022 pour la mise en œuvre d’une solution fixe
So it sounds like it might actually have been placed at 2 different places.
What's odd is that EWA already had a public charger in Storzmatte parking all this time. What exactly where they testing with the additional Mobi-charge unit? They should already know whether they are at capacity or not at the existing station, which is in walking distance of this test site. And they never added any new charger except the semi-public ones in front of EWA Hauptsitz, which were visible on opendata since December 2022.
The address on the marker in 2023 and now is "Obere Zollgasse 74, 3072 Ostermundigen", which doesn't match with the name and coordinates. It might have been another address where Mobi-charge unit #50 has been used after Aarberg.