We introduce the fluctuating Line-of-Sight (fLoS) fading model, characterized by parameters $K$, $k$, $λ$, and $Ω$. The fLoS fading distribution is expressed in terms of the multivariate confluent hypergeometric functions $Ψ_2$, $Φ_3^{(n)}$, and $Φ_3 = Φ_3^{(2)}$ and encompasses well-known distributions, such as the Nakagami-$m$, Hoyt, Rice, and Rician shadowed fading distributions as special cases. An efficient method to numerically compute the fLoS fading distribution is also addressed. Notably, for a positive integer $k$, the fLoS fading distribution simplifies to a finite mixture of $κ$-$μ$ distributions. Additionally, we analyze the outage probability and Ergodic capacity, presenting a tailored Prony's approximation method for the latter. Numerical results are presented to show the impact of the fading parameters and verify the accuracy of the proposed approximation. Moreover, we illustrate an application of the proposed fLoS fading distribution for characterizing wireless systems affected by channel aging.