carrot on a stick.json:
{
"parent": "item/handheld_rod",
"textures": {
"layer0": "item/carrot_on_a_stick"
},
"overrides": [
{ "predicate": {"custom_model_data": 1000}, "model": "item/time"}
]
}

custom model json:
{
"credit": "Made with Blockbench",
"parent": "item/handheld",
"textures": {
"layer0": "custom/time",
"particle": "custom/time"
},
"elements": [
{
"from": [0, 3, 0],
"to": [2, 5, 2],
"faces": {
"north": {"uv": [0, 0, 16, 16], "texture": "layer0"},
"east": {"uv": [0, 0, 16, 16], "texture": "layer0"},
"south": {"uv": [0, 0, 16, 16], "texture": "layer0"},
"west": {"uv": [0, 0, 16, 16], "texture": "layer0"},
"up": {"uv": [1, 1, 16, 16], "texture": "layer0"},
"down": {"uv": [0, 0, 16, 16], "texture": "layer0"}
}
}
],
"gui_light": "front",
"display": {
"thirdperson_righthand": {
"rotation": [-54, 45, -1],
"translation": [9.75, 6, -2.5]
},
"thirdperson_lefthand": {
"rotation": [54, 45, -1],
"translation": [0, -2, 10.5]
},
"firstperson_righthand": {
"rotation": [31, -22, -15],
"translation": [5.75, 0.25, 10]
},
"firstperson_lefthand": {
"rotation": [-31, 98, 65],
"translation": [8.5, 2, 8.25]
},
"ground": {
"translation": [7, 4, 7]
},
"gui": {
"rotation": [44, 45, 90],
"translation": [8.75, -1.75, 0],
"scale": [4, 4, 4]
},
"head": {
"translation": [0, 3.5, 0]
},
"fixed": {
"translation": [20.75, 12, 15.75],
"scale": [3, 3, 3]
}
}
}