In this tikzpicture
\documentclass[margin=2mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning}
\usetikzlibrary{calc}
\usetikzlibrary{shapes.arrows}
\usetikzlibrary{shapes.geometric}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{shadings}
\usetikzlibrary{angles,quotes}
\usetikzlibrary{decorations.markings}
\begin{document}
\begin{tikzpicture}[]
\coordinate [circle, ] (center) at (0,0);
\coordinate (basecenter) at (0,-2);
\coordinate (baseleft) at (-3,-2);
\coordinate (baseright) at (3,-2);
\draw [thick, gray, line width=0.5mm] ($(baseleft) + (-1,0)$) -- (basecenter) -- ($(baseright) + (1,0)$);
\draw [fill=black!20, draw=black!50] ($(baseleft)+(-0.1,0)$) rectangle ($(baseleft) + (0.1,4)$);
\coordinate (TXbottom) at ($(baseleft) + (0.1, 3)$);
\coordinate (TXcenter) at ($(TXbottom) +(0.075,0.3)$);
%\draw [draw=red, fill=red!30!white,rotate=-20] (TXbottom) rectangle ($(TXbottom) + (0.15,0.6)$);
\draw[ draw=red, fill=red!30!white ] let \p1=($(TXcenter)-(center)$),\n1={atan2(\y1,\x1) - 90} in [rotate=\n1] (TXbottom) rectangle ($(TXbottom) + (0.6,-0.15)$);
\draw[thin,blue] let \p1=($(TXcenter)-(center)$),\n1={atan2(\y1,\x1) - 90} in (TXbottom) -- ++(\n1:1.2) coordinate (incliTX);
\path ($(TXbottom) + (0.075,0)$) -- ($(TXbottom) + (0.075,0.6)$) let \p1=($(TXcenter)-(center)$),\n1={atan2(\y1,\x1)-90 } in node[midway, rotate=\n1, ] (inicioTX) {};
\fill[black!70!] (inicioTX) circle (0.05);
\draw[thin,blue] (TXbottom) -- ++(90:1.2) coordinate (vertTX);
\pic [draw, latex-, "$\theta$", angle eccentricity=1.6, angle radius = .75cm,pic text options={shift={(0pt,0.25pt)}}] {angle = incliTX--TXbottom--vertTX};
\draw [line width=1.2mm, draw=yellow!70!brown] ($(center) + (-2.9,0)$) -- ($(center) + (2.9,0)$);
\fill[black!70!] (center) circle (0.05);
\draw [ draw=red,dashed,thick, -> ] (inicioTX) -- (center) coordinate (pabajo);
\end{tikzpicture}
\end{document}
I would like to start the dashed red arrow line from the geometric center of the $\theta$-rotated red rectangle. I have tried to rotate a middle node in the path from the bottom and the top of the red rectangle, but it does not work. The node is still in the no-rotated coordinates (black circle)
Besides, it seems the code is not much efficient and needs some time to compile. I would like to know how to start the dashed line from the rotated red rectangle center.