It does seem to increase motivation to pe. It can certainly have an impact with ed , eq and libido. The amount needed by most guys to function normally is above the bottom level of the "normal" range . Do not be satisfied if your doc says normal get the numbers.
I believe from the literature I've read testosterone plays a big part in overall EQ, and also maintains the inner spongy bodies of the penile chambers, keeping them flexible and healthy and thereby keeping blood flow inside the penis in healthy levels as well. Also I read in literature testosterone is responsible for the basic functions of an erection: the properly opening and closing of the valves which let blood flow in, the tightening of the blood flow so blood doesn't leaks out after erection has been achieved etc.
Testosterone deficiency means impaired blood flow which means less supply of oxygen and nutrients the penile tissue needs to heal the micro-tears that PE creates in order to make the penis bigger.
One can hypothise this way that the more testosterone you have, the better your EQ will be, and the better PE gains are achieved, and the better the penis functions overall.
Using a testosterone booster won't necessarily help in each person's case, and when one stops supplementation, the boosting dissapears to. An exception in my opinion is vitamin D3, which acts more like a hormone in your blood and is supposed to be maintained at a certain level in order to be effective. We normally get D3 from the sun but because of the climate this could be impaired and supplementation orally could be practical. D3 is responsible for blood thinning to a certain extent, and also is our body's own estrogen inhibitor. (the counter-hormone of testosterone)
In all other cases one should look at the body itself, the current health status of one's body, the amount of muscle (the more muscle, the more testosterone you'll have) any abnormalities of the scrotum where testosterone is mainly produced etc.
Also phosphatidylserine, a nootropic is shown to raise testosterone in vivo studies with humans, because it heals and improves the part of the brain which is co-responsible for the body mechanism that creates testosterone, which the scrotum is also a part of, or better said the testicles inside the scrotum.
Other than those, main nutrients are required in adequate amounts in the body in order for the body to optimally create testosterone as it is supposed to do. Certain deficiencies in basic nutrients could be responsible for impaired testosterone production.
While test deficiency would be expected to hurt pe there is no evidence that supra normal levels helps it . Or even that upper normal is better than normal . Lower normal can be problematic as I believe it is set too low,
From what I have seen eq and general function can be at peak levels on modest levels of test .
Vit d is commonly undersupplied and a test for body levels is a good idea particularly if you live in a cool climate.