Can't understand why oscilloscope requires incomplete circuit in order to measure voltage in secondary winding of very low inductance transformer
The  transformer must not load the impedance of the source more than 10% of rated load. We call this the excitation current.  

Otherwise if primary impedance is low then the secondary impedance will also be low but determined by a turns ratio \$n^2\$  . Then if mutual coupling is low, you don't get much signal out.

Then capacitive coupling from the primary to secondary windings permits you to see a potential signal coupled to the secondary.  But as soon as it is grounded or connected to a load, the signal would drop because of poor mutual coupling.  then ensure Self Resonant Frequency is much greater than application from interwinding capacitance.







simulate this circuit &ndash; Schematic created using CircuitLab

See how grounding the other side in this case, shorts out the capacitance.   Try reversing the secondary windings and see if it changes slightly.

Estimate the impedance or each component, R, L C and load to understand why you need to ensure the primary impedance is 10x higher than lowest load impedance (referred to input) for 10% load regulation.  ( typical)