First, if you have an empty reservoir side you almost certainly have a dead pump for that side if the car has been used for any period of time while that condition existed. As you've already been told, it's got to be a leak, and a serious one, in the system to completely drain the reservoir.
It is not at all unusual for the fluid to darken in these cars, and by darken I do not mean "to go opaque" but to slowly take on a somewhat browner tone due to rust in the system. The fluid should be changed a minimum of once every two years in non-humid climates and annually if you live somewhere where it's very humid.
From your description I would also strongly suspect the possibility of damage to the mesh filter screens in the bottom of the reservoir due to crud collecting over years of lack of maintenance. This photo isn't from either of my cars, but the reservoir in the Silver Wraith II I purchased in January had plenty of "algae like" material in the reservoir. The color of the fluid in the "clear" reservoir of that car was about the color of tea. The original fluid in my Shadow II had gotten that dark, too, but did not have any solids in it.
The original design for the filter screens under the baffles in the reservoir allows them to collapse and develop holes, potentially allowing some really nasty solids to circulate through the system and block any number of incredibly tiny passages. Here's an image of an original filter that has been damaged and the core of a new design of my own (which doesn't yet have its mesh applied) that will never collapse. It may clog, and then trigger insufficient pressure and a warning light, rather than pollute the entire system.
And with the stainless mesh applied and affixed into place using polypropylene cord. I've tried metal wire but do not prefer it to the cord, which is easier to work with and about as resistant to any sort of damage that a substance can be.
Instructions for flushing and bleeding your brake/hydraulic system are available in Flush and Bleed Your Silver Shadow/Bentley T Hydraulics/Brakes the Easy Way
Brian, who notes you may need a power bleeder if your car has a master cylinder in the rat trap (earlier Shadow series).