In this paper, we propose a deep learning-based signal detector called TransD3D-IM, which employs the Transformer framework for signal detection in the Dual-mode index modulation-aided three-dimensional (3D) orthogonal frequency division multiplexing (DM-IM-3D-OFDM) system. In this system, the data bits are conveyed using dual-mode 3D constellation symbols and active subcarrier indices. As a result, this method exhibits significantly higher transmission reliability than current IM-based models with traditional maximum likelihood (ML) detection. Nevertheless, the ML detector suffers from high computational complexity, particularly when the parameters of the system are large. Even the complexity of the Log-Likelihood Ratio algorithm, known as a low-complexity detector for signal detection in the DM-IM-3D-OFDM system, is also not impressive enough. To overcome this limitation, our proposal applies a deep neural network at the receiver, utilizing the Transformer framework for signal detection of DM-IM-3D-OFDM system in Rayleigh fading channel. Simulation results demonstrate that our detector attains to approach performance compared to the model-based receiver. Furthermore, TransD3D-IM exhibits more robustness than the existing deep learning-based detector while considerably reducing runtime complexity in comparison with the benchmarks.