  We study the percolation configuration arising from the random current
representation of the near-critical Ising model on the complete graph. We
compute the scaling limit of the cluster size distribution for an arbitrary set
of sources in the single and the double current measures. As a byproduct, we
compute the tangling probabilities recently introduced by Gunaratnam,
Panagiotis, Panis, and Severo in [GPPS22]. This provides a new perspective on
the switching lemma for the $\varphi^4$ model introduced in the same paper: in
the Gaussian limit we recover Wick's law, while in the Ising limit we recover
the corresponding tool for the Ising model.
