Eliashberg & Gromov sketched a proof in their paper [*"Convex symplectic manifolds"*][1] (Section 3.4). Written in the 4-dimensional case it says:

For $r>0$ define the subspace $X(r)\subset\mathbb{R}^4$ to be the union of the half-space $\lbrace q_2<0\rbrace$ and the half-space $\lbrace q_2>0\rbrace$ and the 3-ball $\lbrace(p_1,p_2,q_1,0)\;|\;p_1^2+p_2^2+q_1^2<r^2\rbrace$. For $R>r$ there is no 1-parameter family of symplectomorphisms $S(t):B(0,R)\to (X(r),\omega_\text{std})$ with the image of $S(0)$ in $\lbrace q_2<0\rbrace$ and the image of $S(1)$ in $\lbrace q_2>0\rbrace$.

McDuff & Traynor (*"The 4-dimensional symplectic camel and related results"*) go on to show that $X(r_1)$ and $X(r_2)$ are symplectomorphic if and only if $r_1=r_2$.

[1]: https://www.ihes.fr/~gromov/wp-content/uploads/2018/08/976.pdf