Details are open for interpretation which is what you are really after.
copyright infringement let me summarize.

Current controversies in testosterone testing: aging and obesity
Elin RJ, Winters SJ
Clinics in Laboratory Medicine - March 2004 (Vol. 24, Issue 1, Pages 119-139

Testosterone circulates in the plasma in the free form but also in bound to
protein carriers so the total testosterone may not be the ideal specimen.

Controversies exist about the accuracy and interpretation of clinical
laboratory tests to evaluate sex hormone production and function,
particularly in obese and elderly men for the problems you stated.

The ideal specimen is one collected in morning between 8 and 10.
A circadian rhythm exists where it is highest in the morning and some say
that is when other hormones are also high causing some heart attacks.

. The difference in the concentration between the lowest and the highest is
approximately 15%, but may be as much as 50%. The pulsatile frequency of
testosterone secretion about once per hour but the pulse amplitude is low
with small fluctuation in the blood concentration

The total testosterone concentration may be insufficient to appropriately
evaluate testosterone deficiency in certain clinical situations, such as
obesity and older men and also in men who have hyperinsulinemia or hyper- or
hypothyroidism and men who are on antiepileptic drugs. Like other serum
analytes that are protein bound, such as total calcium and total thyroxine,
the amount of the binding protein may effect the measurement of the total
concentration of the analyte; only the free analyte has biologic activity.
In men, approximately 44% to 65% of testosterone is bound to SHBG, a
high-affinity but low-capacity binding protein and about 33% to 50% is bound
primarily to albumin with a high capacity but low affinity. The total
testosterone concentration in plasma is related directly to the SHBG
concentration in men. Several factors affect the concentration of SHBG in
plasma and, thus, influence the total testosterone concentration. The bias
in the total testosterone concentration that is due to SHBG in certain
clinical situations supports the determination of the free testosterone or a
surrogate test/index.