Do you think it's OK to run Power Brake Pump all the time?

The first thing to check: The two 30 Amp fuses should have power supply (+12 V) all the time; the 3 Amp fuse gets +12 V when the ignition switch is turned to the first position (accessories on, ignition still off). If the pump does not start running, you can bring +12 V directly to the 3 Amp fuse and see if the pump runs then (before testing, pump the brake pedal a few times to release pressure and activate the pressure switch).

Since you got the pump running briefly when you fiddled with the fuses, you my have a corroded contact at the fuse or relay pins and sockets; especially check the contacts of the 30 Amp fuses and relays for any signs of burning/melting. (Note: The three relays are very different, make sure you don't accidentally swap them)

 

I did a 3 part video on the basics of the ABS system. This should get you to part 1: https://m.youtube.com/watch?v=B3RH5uTXrqI
As you have found out it's a bit of a maze to dig through. The other problem is those damn relays are Ferrari specific. Not easy to find, not cheap, and not replaceable with something from AutoZone. Agree with above; unplug and clean all contacts and check all fuses and pray. If still nothing you'll have to go through each component from the pressure switch, through the relays and diode box to the pump. Good luck!

 

While you are checking things out may want to also check the wiring harness and connectors.

There are fuses and wiring harness available in the FChat classified ads section if needed.

 

The top relay should not be a problem to find - must have 87 & 87a pins.
The middle one is basically a simple 4-pin relay - you can add diodes outside in the orientations as shown.
The bottom one is same as the top one, just add diodes outside.
Note the orientation of the diodes, not same on the middle and the bottom relays. Diodes 1N4005, 6 or 7 will do as they are for 1 Amp and the relay draws about 0.1 Amp. All mentioned diodes are good for 400 Volts or more which is required in order that they can handle the backlash voltage pulse of the relay coil on switch-off which can be as high as 200-300 Volt.
Image Unavailable, Please Login

 

The yellow relay is there only to disable the ABS system during cranking (to unload the battery). It provides power to the ABS system when it is OFF via its 30 to 87a pins which are normally closed (closed when the relay is OFF); during cranking, its coil is energised (relay ON) and it temporarily disconnects the power to the ABS system. Looks like your yellow relay is faulty. i.e. does not provide continuity from pin 30 to pin 87a (when in OFF position). You can pull it out and check whether there is continuity 30 to 87a. If not, I think it can be opened and you can then clean the contacts that are in closed position.

For a quick check, you can (with the yellow relay removed) plug a short piece of wire, one end into the socket of pin 30 and the other end into the socket of pin 87a (create a by-pass) and see if the ABS works fine then.

With regard to your energising the black relay by the ignition "on", it is o.k. if the pump stops working by itself after some time, comes on again after you pump the brake pedal a few times and goes off after you have stopped pumping. However, your ABS may not function in this case but you may have brake boost only.

 

This is a detail (from the wiring diagram for 348) showing interconnection of the Yellow and Black relays. In its OFF position (and the ign. key in 1st position and also in ign. position i.e. when the engine is running), the Yellow relay energises the Black relay and provides power to the ABS ECU (to Pin 2). If your bringing of the ignition switched supply is to the Pin 86 of the Black relay, then you have done the same as what the Yellow relay normally does, via Pins 30 & 87a when in OFF position, and your ABS will function normally. The only function you will not have is the temporary cut-off to the ABS ECU and the ABS pump during cranking (to unload the battery) when the Yellow relay is switched ON cutting the link 30-87a.
Image Unavailable, Please Login

 

A blue Volvo relay (shown on the pics) can be used to replace any of the ABS relays. This relay already has one internal diode, across pins 85 - 86, in the correct orientation. It is also easy to open. The slight mods would be as follows:

1. For the Yellow Relay - insert a diode into the wire going to relay Pin 86 (cathode towards the relay pin)

2. For the Black Relay - insert a diode into the wire going to relay Pin 85 (anode towards the relay pin); Note: Pin 87a of the relay will not be used in this case; it can be cut off or left as I think the socket for it is empty.

3. For the Green Relay - cut out the diode inside the relay (see 3rd pic)
Image Unavailable, Please Login
Image Unavailable, Please Login
Image Unavailable, Please Login