Can a reaction have carbocation resonance followed by a hydride shift?
Substituted cyclopentadienes are an unique molecules, which are not stable at room temperature (recall dimerization). For example, 1-methylcyclopent-1,3-diene (1) or 2-methylcyclopent-1,3-diene (2) or 5-methylcyclopent-1,3-diene (3; diene in the question) would rearranges to a mixture of all 3 positional isomers if leave at room temperature for 1-2 days by hydrogen migration (Ref.1 &amp; 2). The abstract of Ref.1 states that:


  A number of substituted cyclopentadienes display characteristic properties which are representate of all members in the series: (a) the endocyclic double bond isomers are in the thermodynamic equilibrium; the process of establishing the equilibrium being retarded; (b) the transformation of isomeric cyclopentadienes proceeds by steps, i.e. a proton from the methylene group (5th position) passes mainly to the adjacent C-atom (1st position). The proton-cyclopentadienyl anions are probably transitional states in the transformation of isomers. It is assumed that this transformation is a first order reaction. As a result of this investigation it has been shown that the structure of the substituted cyclopentadiene (or the composition of the isomer mixtures) depends mainly on the character of the substituent and not on the method of synthesis.


The ratio of 1 : 2 : 3 would be 45:54:1. Kinetically, the process is first order and activation energy is $\pu{20.4 kcal/mol}$ over temperature range of $\pu{298-313 K}$ (Ref.3). The kinetic studies by NMR has been suggested that rearrangement is due to 1,2-hydrogen shift (Ref.4).

Yet, these cyclopentadienes are also suseptible to protonation by strong acids (Ref.5). Thus, it is very possible that protonation at $\ce{C1}$ 1,5-addition after 1,2-hydride migration. However, as explained above, 5-methylcyclopent-1,3-diene (3) is relatively the least stable positional isomer. At room tempeature, it would stay mostly as 1-methylcyclopent-1,3-diene (1) and 2-methylcyclopent-1,3-diene (2) with $\approx 1:1$ ratio. Therefore, addition would be either 1,4- and 1,2-.



References:


V. A. Mironov, E. V. Sobolev, A. N. Elizarova, "Some general characteristic properties of substituted cyclopentadienes," Tetrahedron 1963, 19(12), 1939-1958 (https://doi.org/10.1016/0040-4020(63)85008-5).
Sigmund M. Csicsery, "Methylcyclopentadiene Isomers," J. Org. Chem. 1960, 25(4), 518-521 (https://doi.org/10.1021/jo01074a009).
Raymond K. Crandall, “Investigation of the electronic and thermal rearrangement properties of spiro[2,4]hepta-4,6-dienes,” M.S. Thesis, Rochester Institute of Technology, Rochester, NY, 1982.
S. McLean, P.Haynes, "Hydrogen migration in cyclopentadienes," Tetrahedron 1965, 21(9), 2329-2342 (https://doi.org/10.1016/S0040-4020(01)93887-6).
Ronald F. Childs, Maung Zeya, “Diprotonation of 5-Acyl-1,2,3,4,5-pentamethylcyclopentadienes,” Can. J. Chem. 1975, 53(22), 3425-3430 (https://doi.org/10.1139/v75-490)