The thing with the updated BIOS bugged me so I have downloaded the oldest version I could find, reflashed it and voila - the turbo button works fine. Sorry for the thread... I truly thought that I have tried everything when posting it.

I have a problem with Turbo button, it doesn't work. If I toggle Turbo via keyboard (Ctrl Alt +/-) it works, benchmark shows about one quarter speed drop. Now the most strange thing, Turbo LED is connected to the motherboard (TB_LED pins), if I toggle Turbo via kbd the TB LED is On at turbo and Off at de-turbo, so far so good, but if I toggle Turbo by button (connected to TB_SW pins on MoBo) it also switch On/Off Turbo LED, but the cpu speed in benchmark does not change!
Below are listed HW details of my setup. I also tried older bioses (oldest one tested was 1.022B100 which was originally inserted in the board). Now I don't know if its is some HW fault with this board, or general bug, or something different. In the post above someone has the same problem with different MoBo, but the same chipset.
Could someone please confirm that the turbo button on this board ever worked?

Motherboard FIC 486-PIO2 rev. K1.2, actual BIOS v 1.15C101, chipset VIA VT82C496G/VT82C505
CPU tried so far: i486DX4-100 (WT), i486DX2-66 SX911 (WT), i486DX2-66 SX955 (WB/WT)

The BIOS must have a setting to enable/disable the Turbo switch. Ensure it's enabled, and your turbo switch will become effective again.

Unfortunately, none of the BIOS versions I tried had an accessible Turbo/switch setting.
My first step is to find out if anyone has ever had the turbo switch working on this board and to find out if it is a hardware defect on my board. It is strange that the Turbo LED signals the status according to the Turbo SW, it seems that the input is OK but the problem is somewhere else.

I wonder if it's BIOS related or Via chipset related in general. I have switched to SiS chipsets for 486 boards and never looked back.

Does the BIOS have an option to choose the clock source (ICLK/SCLK or something like that?)

The BIOS is quite poor in terms of the number of available options, I couldn't find any clock source selection.

By the way, I dug through some user manuals for motherboards with the same chipset and for the Chaintech 4UPB type, the turbo SW functionality is interesting:
1-2 open: high/low speed changed by keyboard
"CTRL - ALT - +" set to high speed
"CTRL - ALT - -" set to low speed
1-2 short: always high speed

...but I also tried this option and it still didn't work.
I would like to know if anyone has a turbo switch working on this board.

Small update. I load the bios image 115C101 into modbin and looked at turbo/speed settings.
It looks like the speed seting is enabled in general (via KBD I'm able to change hi/lo speed), but the "Turbo Switch Input: Disabled" seeting in bios means that the input for turbo button is inactive. Am I right?
So it would be possible to mod the bios and enable turbo button. Could someone more experienced with bios tweaking advise what setting would be appropriate?

Sounds about right. It shouldn't hurt to try enabling it and see what happens.