You need to understand voltage, current, resistance, and current regulators. Read some Wikipedia articles and look for tutorials on those keywords.
The TCDS circuit tries to make current flow in a load. In this application, this load is the subject's cranium, and salt water to ensure good connections (minimum resistance). I will call this a "wired cranium"
The electrical behaviour of biological material is far too complex to fully describe as a resistance, but it can be loosely approximated as a resistance. You measured 6 kilohms. That sounds about right.
Voltage, current, and resistance are related through an extremely important - probably the most fundamental - law used in electronics: Ohm's Law. It states:
I = V / R. (Rearranges to . . R = V / I . . . and V = I x R.)
I is current (which flows THROUGH wires and components) measured in amps;
V is voltage (which is measured BETWEEN two points in a circuit), in volts, and
R is resistance (which is a characteristic of resistors and some similar components), measured in ohms.
Notice that current is always measured in amps in that formula. This is inconvenient because we're dealing with milliamps. But if we measure resistance in kilohms instead of ohms, we can measure current in milliamps - the opposite rescalings of resistance and current cancel each other out and Ohm's Law still works.
So let's plug some numbers in. Let's consider the wired cranium to be a 6k resistor and say we want to feed a DC current of 1 mA through it. We can calculate the voltage using the rearrangement of Ohm's Law: V = I x R. Using milliamps and kilohms, we get:
V = I x R
= 1 * 6
= 6V.
This means that if we apply 6V DC between those electrodes, 1 mA of current will flow through the subject's cranium. If we apply 9V DC, 1.5 mA of current will flow. If we want to cause more than 1.5 mA to flow, we need more voltage. A single 9V battery cannot cause more than 1.5 mA to flow in a wired cranium with a resistance of 6k. The current is limited by the resistance of the wired cranium.
Actually, adding the current regulator circuit drops some voltage, so using a 9V power source, you might only get 1.4 mA to flow through the wired cranium.
Let's say you have set your current regulator for 4 mA test current. But if your circuit has a 9V battery, and the wired cranium resistance is 6k, it's impossible to cause 4 mA of current to flow. The actual current flow will never be more than about 1.4 mA.
In that situation, the current regulator can be described as "saturated", or "out of regulation". The current regulator tries to pass 4 mA but the load resistance is so high that it can't provide enough voltage (because it is limited by its battery voltage) to cause 4 mA to flow.
In this state, with the original design with the LED, the LED would go out, indicating that the current regulator is "out of regulation", and the actual cranial current is not as high as the value selected on the control potentiometer in the current regulator.
There are two ways to get more current to flow: increase the battery voltage, or decrease the wired cranium resistance.
I would try the second idea first. See what you can do with larger contact areas, and more salt water. I have no experience with attaching electrodes to people, so please look elsewhere for advice on that subject.
Increasing the battery voltage might cause subjects to feel an electric shock sensation when the electrodes are first applied, unless the circuit is switched off until the probes are firmly attached to the subject. In any case, the idea makes me uncomfortable.
The values I suggested for the current-setting components in the two-transistor circuit - about 150 ohms for the fixed resistor and 1k for the variable resistor - will give a current range from about 0.6 mA to about 4.3 mA.
If you want to test wtih 4 mA and your circuit uses a 9V battery, you will need a wired cranium resistance of 2 kilohms or less. I calculated this from another rearrangement of Ohm's Law: R = V / I, where R is resistance in kilohms, V is voltage (I'll assume about 8V because of the 1V dropped by the current regulator) and I is current in millamps.
R = V / I
= 8V / 4 mA
= 2 kilohms
You will need to make much better contact with the subject to reduce the resistance from 6k to 2k.
My opinion on the 5 mA fuse is that it is absolutely essential. Remember, you are connecting this device to a human being. Any of a number of things could concievably go wrong with the device and cause excessive current to flow. Neglecting to install and replace safety components because of their cost is highly irresponsible.