If the official link is dead, search for: on the Toshiba BIOS Collection on Archive.org. Final Pro Tip for PSLF8L Owners: This laptop has a dual BIOS chip – but only if you’re lucky. Most PSLF8L units have a single SPI flash. Do not interrupt the flash even if the screen goes black for 2 minutes. Wait 5 minutes minimum.
You can hot-flash the BIOS if you have an SPI programmer (CH341A) – ask in specialized forums like Badcaps.net . update bios for toshiba satellite l510 pslf8l