[kaptain]

No the tool is not absolutely necessary.

The red fluid near the fan motor IS hydraulic fluid, not coolant. It can leak from the fan motor connections, or the seals in the Overhung Load Adaptor, which is the gearbox between the fan motor and the fan.

Clean the area with brake cleaner. Then take small sections of white paper towel and zip tie in strategic locations. Keeping in mind that fluids don’t flow up hill. The white paper towel is a very quick visual when the red hits it. By the way, Newell uses Auto Transmission Fluid for the hydraulic fluid.

Thank you, Richard. You are right. The more I examined and looked for the source of the leak, the more it appears to me the leak is hydraulic fluid. 
I am still trying to figure out the source of the leak. It's a very small, tiny seeping leak. 

You said: "Newell uses Auto Transmission Fluid for the hydraulic fluid.", I looked up on NAPA and amazon, and there appear lots of choices in this category.
I wonder if there is any particular type or make that Newell recommends? 
Is this one good choice?  https://www.amazon.com/Valvoline-Multi-V...B008QDV2JG